Chaos and Fractals
type: channel
description: Chaos and Fractals is a peer-reviewed interdisciplinary journal dedicated to advancing the understanding and application of chaos theory and fractal geometry across various scientific disciplines. The journal serves as a nexus for researchers, mathematicians, physicists, engineers, and practitioners to disseminate cutting-edge research findings, innovative theories, and practical applications in the realm of chaos and fractals. Chaos and Fractals publishes original research articles, review papers, technical notes, and case studies covering a wide range of topics, including but not limited to: - Dynamics of Nonlinear Systems - Fractal Geometry and Applications - Chaotic Behavior in Natural and Artificial Systems - Complex Systems Modeling and Analysis - Nonlinear Dynamics in Biological Systems - Fractal Imaging and Image Analysis - Applications of Chaos and Fractals in Physics, Engineering, Biology, and Social Sciences - Chaos-Based Cryptography and Secure Communications - Fractal-Based Signal Processing and Analysis Our journal aims to foster interdisciplinary collaboration and facilitate the exchange of ideas among researchers and practitioners working in the fields of chaos theory and fractal geometry. We welcome contributions that explore theoretical developments, computational methods, experimental observations, and practical implementations related to chaos and fractals. Chaos and Fractals is committed to upholding the highest standards of scholarly excellence and integrity. All submissions undergo rigorous peer review by experts in the field to ensure the quality, validity, and significance of the published work. We invite researchers and practitioners from around the globe to join our community and contribute to the advancement of chaos theory and fractal geometry for the betterment of science and society.
publisher: adbascientific
language: en
publication name: Chaos and Fractals
issn: 3023-8951
copyright: The following copyright agreement is read and approved by authors before they publish their work to our journal's online system. The copyright notice text is regarded to have been approved by them after they give their approval. Copyright Notice Text Author(s); a) The submitted article is the original work of the author(s), and they do not plagiarize, b) All authors have participated in this study individually, and they take all responsibility for the study. c) All authors have seen and approved the final version of the submitted article, d) The article has not been published elsewhere or submitted for publication, e) They accept and undertake that the text, figures, and documents in the article do not violate the copyrights of other parties. The authors are deemed to have accepted the following terms by submitting their work to the journal under the CC BY-NC license. The copyright of the published article belongs to its author under CC BY-NC 4.0 license. The authors authorize the journal to publish the article and identify itself as the original publisher. The authors grant the right to freely use the article to any third party as long as the original authors and citation details are identified. Nothing in this license impairs or restricts an author's right to preserve the integrity and ownership of their work. All commercial rights related to the article belong to the authors. The authors own the copyright of their work published in CHF, and their work is licensed under Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0). The Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license allows the work to be shared, copied, and reproduced in any size and format except for commercial use. It also allows it to be rearranged, transformed, and adapted, including building upon the original work, with proper reference to it. CC BY-NC 4.0: https://creativecommons.org/licenses/by-nc/4.0/ The license owner cannot cancel these r…
items: An Investigation into the Interpretation of Pi (π) as the Arithmetic Mean of the Golden Ratio (ϕ) and the Feigenbaum Constant (δ)
items: Nonlinear Effects of Zero-Crossing Detection Based Firing Angle Power Control on Lighting Performance
items: Evaluation of Deep Learning Architectures for Pulmonary CT Lesion Classification Highlighting Diagnostic Performance
items: A Comparative Performance Analysis of Linear Congruential and Combined Linear Congruential Generators
items: Design and Performance Evaluation of a Hybrid PRNG: Gold-SA II Optimized LFSR Combined with Discrete Chaotic Maps
items: Cost-Effective Hardware Realization of Chaotic Systems via High-Performance STM32 DAC Interface
items: Ad-Click Prediction Enhanced by Nonlinear Dynamics-Inspired Feature Extraction and Ensemble Optimization
items: Nonlinear Dynamics and Chaos Control in a Discrete Sel'kov Model with Substrate Inhibition
items: Attack-Resistant Chaotic Communication System in Non-ideal Physical Channel
items: Partial Prey Migration as a Non-autonomous Harmonic Oscillator: Chaos-Order Transitions in a Forced Classical Lotka-Volterra Model
items: Dynamical Analysis of Barium Titanate Crystal in Alternative Voltage RL Circuit
items: A Study on Hindmarsh-Rose Neurons Under an Electric Field
items: Synergistic Construction of High-Performance S-Boxes based on Chaotic Systems: A Paradigm Shift in Cryptographic Security Design
items: A Two-Memristor-based Chaotic System with Symmetric Bifurcation and Multistability
items: Permanent Magnet Synchronous Motor with Load Torque: Dynamics, Circuitry Execution and Control
items: FPGA-Based Chaotic Oscillator Designs and Performance Analysis
items: Investigation of the Impact of Alloying Elements on the Mechanical Properties of Superalloys Using Explainable Artificial Intelligence
items: A Novel Chaos-Based Encryption Technique with Parallel Processing Using CUDA for Mobile Powerful GPU Control Center
items: Digital Implementation of Chaotic Systems Using Nvidia Jetson AGX Orin and Custom DAC Converter
items: Numerical Exploration of a Network of Nonlocally Coupled Josephson Junction Spurred by Wien Bridge Oscillators
items: Comparative Analysis of State-of-the-Art Q&A Models: BERT, RoBERTa, DistilBERT, and ALBERT on SQuAD v2 Dataset
items: Analysis of a Resistive-Capacitive Shunted Josephson Junction with Topologically Nontrivial Barrier Coupled to a RLC Resonator

An Investigation into the Interpretation of Pi (π) as the Arithmetic Mean of the Golden Ratio (ϕ) and the Feigenbaum Constant (δ)
type: item
description: This study comprehensively examines the numerical proximity of the arithmetic mean of the golden ratio (ϕ) and the Feigenbaum constant (δ) to the number π, the theoretical mechanisms underlying this relationship, and its epistemological value. Although these three fundamental constants, situated at the intersection of mathematics and theoretical physics, are generally treated as elements of independent disciplines, this research unearths a unique structural bridge expressed through the formulation π = (ϕ + δ)/2. Numerical analyses prove that the relationship in question can be evaluated within the class of high-precision mathematical approximations, with a notably low relative error margin of approximately %0.064. Within the scope of the study, the fact that the arithmetic balance between the "most irrational number" ϕ, representing maximum dynamic stability, and the universal scaling factor δ, defining the critical threshold at which systems drift into chaos, corresponds to the number π the foundation of periodic cycles is discussed within the framework of the "geometric balance between chaos and order" hypothesis. Whether this numerical pattern is a coincidental numerological coincidence or a yet to be discovered deep topological necessity is analyzed in the context of dynamical systems theory and Euler’s identity. In conclusion, by presenting a simple and elegant equation that has gone unnoticed in the half century since the discovery of the Feigenbaum constant, this article raises new epistemological questions regarding the nature of fundamental constants and offers an interdisciplinary perspective on understanding the hidden geometry of nature.
subject: Articles
  topic: section
subject: Chaos
  topic: keywords
subject: Mathematical constants
  topic: keywords
subject: Transcendental numbers
  topic: keywords
subject: Pi (π)
  topic: keywords
subject: Golden ratio (ϕ)
  topic: keywords
subject: Feigenbaum constant (δ)
  topic: keywords
subject: Mathematical constants
  topic: subjects
subject: Mathematics
  topic: disciplines
creator: İhsan Pehlivan
creator: Selahattin Bulut
creator: Emin Güney
rights: Copyright (c) 2026 https://creativecommons.org/licenses/by-nc/4.0/
date: 2026-01-31
publication date: 2026-01-31
starting page: 61
ending page: 64
doi: 10.69882/adba.chf.2026019

Nonlinear Effects of Zero-Crossing Detection Based Firing Angle Power Control on Lighting Performance
type: item
description: This paper presents the design, development, and performance evaluation of a single-phase microcontroller-based SCR (Silicon Controlled Rectifier) power control system employing a Zero-Crossing Detection (ZCD) technique for precise AC power regulation. The proposed embedded hardware architecture integrates a ZCD-based control unit, a bidirectional SCR driver circuit, and an SCR module with a power conditioning unit. The control algorithm, implemented on a microcontroller platform, performs precise zero-cross detection via hardware interrupts, computes the firing angle (α), and generates synchronized triggering pulses through optically isolated driver circuits. The system supports multiple operational modes, firing angle control, integral cycle control, and on/off control, enabling flexible load management. Experimental validation was performed using resistive loads and a 220 V, 42 W incandescent bulb. The results demonstrate accurate bidirectional triggering and stable load voltage control across firing angles from 0° to 180°, corresponding to delay times (td) of 0–10 ms. Notably, the measured RMS voltage, apparent power and perceived illumination reached their peak at α = 45°, confirming a non-linear relationship between the firing angle and output characteristics. The developed prototype provides rapid and stable power regulation between 0% and 100%, making it suitable for industrial heating and lighting systems. Future research will incorporate adaptive and soft-start control strategies to enhance operational efficiency and compatibility with resistive–inductive loads.
subject: Articles
  topic: section
subject: Zero crossing detection
  topic: keywords
subject: Firing angle control
  topic: keywords
subject: Nonlinearity
  topic: keywords
subject: Embedded system
  topic: keywords
subject: Power Control
  topic: subjects
subject: Electronics and Computer Science
  topic: disciplines
creator: Dursun Kerem Karaduman
creator: Kenan Gençol
creator: Serkan Dişlitaş
rights: Copyright (c) 2026 https://creativecommons.org/licenses/by-nc/4.0/
date: 2026-01-31
publication date: 2026-01-31
starting page: 54
ending page: 60
doi: 10.69882/adba.chf.2026018

Evaluation of Deep Learning Architectures for Pulmonary CT Lesion Classification Highlighting Diagnostic Performance
type: item
description: Early identification of pulmonary lesions is a critical factor in enhancing patient prognosis and survival rates. This study systematically evaluates the diagnostic performance of five deep learning architectures, ConvNeXt Base, ResNet50, EfficientNetV2 Small, InceptionV4, and Xception, for the three-class categorization of Computed Tomography (CT) scans into Benign, Malignant, and Normal categories. Utilizing the public IQ OTH NCCD dataset, we applied a transfer learning approach with ImageNet weights, complemented by a robust training pipeline incorporating dynamic data augmentation and early stopping to mitigate overfitting and ensure model generalization. Model efficacy was rigorously assessed on an independent test set using accuracy, precision, recall, and F1-score metrics. Experimental results indicate that InceptionV4 emerged as the most reliable architecture, achieving an overall accuracy of 0.988 and a macro-averaged F1-score of 0.976. Notably, this model demonstrated perfect sensitivity for the pathologically critical malignant class, achieving a recall rate of 1.00, thereby prioritizing clinical safety. These findings confirm that advanced neural networks can serve as dependable secondary opinion systems for clinicians. Given its superior sensitivity and balanced diagnostic profile, InceptionV4 represents a promising candidate for integration into automated lung cancer screening workflows to improve diagnostic precision.
subject: Articles
  topic: section
subject: Lung cancer
  topic: keywords
subject: Deep learning
  topic: keywords
subject: Computed tomography (CT)
  topic: keywords
subject: InceptionV4
  topic: keywords
subject: Transfer learning
  topic: keywords
subject: Medicine
  topic: subjects
subject: Computer Engineering
  topic: disciplines
creator: Ugur Bahtiyar Guven
creator: Yiğitcan Çakmak
creator: Ishak Pacal
rights: Copyright (c) 2026 https://creativecommons.org/licenses/by-nc/4.0/
date: 2026-01-31
publication date: 2026-01-31
starting page: 47
ending page: 53
doi: 10.69882/adba.chf.2026017

A Comparative Performance Analysis of Linear Congruential and Combined Linear Congruential Generators
type: item
description: The generation of high-quality randomness is a fundamental prerequisite for the integrity of stochastic modeling and numerical simulations across various scientific disciplines. As the complexity of computational experiments grows, the robustness of the underlying Pseudo-Random Number Generators (PRNGs) becomes a decisive factor in preventing systematic biases. This study examines the performance and reliability of PRNGs, focusing on the widely utilized Linear Congruential Generator (LCG) and the Combined Linear Congruential Generator (CLCG), which was developed to address the inherent limitations of the former. Using a simulation environment implemented in Python, both algorithms were evaluated based on visual distribution analysis (histograms and 2D/3D scatter plots), statistical fitness (Chi-Square and autocorrelation tests), and computational efficiency (execution speed). The empirical findings demonstrate that while the LCG operates approximately 2.1 times faster than the CLCG, it exhibits a distinct "lattice structure" in multi-dimensional space, leading to significant structural correlation errors. In contrast, the CLCG method, despite its higher computational overhead, achieved a high p-value of 0.92 in the Chi-Square goodness-of-fit test, indicating near-perfect alignment with the theoretical uniform distribution and minimized sequential dependency. Consequently, this study concludes that CLCG is a more reliable choice for high-precision simulations, whereas LCG remains viable for simple applications where computational speed is the primary constraint.
subject: Articles
  topic: section
subject: Pseudo random number generators
  topic: keywords
subject: LCG
  topic: keywords
subject: CLCG
  topic: keywords
subject: Simulation
  topic: keywords
subject: Performance analysis
  topic: keywords
subject: Computer Sciences
  topic: disciplines
creator: Ahmet Esad Eldoğan
creator: Abdullah Sevin
rights: Copyright (c) 2026 https://creativecommons.org/licenses/by-nc/4.0/
date: 2026-01-31
publication date: 2026-01-31
starting page: 21
ending page: 28
doi: 10.69882/adba.chf.2026014

Design and Performance Evaluation of a Hybrid PRNG: Gold-SA II Optimized LFSR Combined with Discrete Chaotic Maps
type: item
description: Random Number Generators (RNGs) play a critical role in ensuring data security in cryptographic systems. Linear Feedback Shift Registers (LFSRs) are widely used due to their hardware speeds and low costs; however, their linear structures make them vulnerable to algebraic attacks and may yield insufficient results in statistical randomness tests. This study proposes a hybrid architecture based on optimisation and chaos to enhance the cryptographic security of LFSR-based generators. The irreducible polynomials and initial seed values that provide the maximum period length of the LFSR have been optimised using the Modified Golden Sine Algorithm (Gold-SA II). As the raw LFSR outputs failed the NIST SP 800-22 tests, the system was supported by a chaotic final processing layer containing Sine, Chebyshev, Logistic, Tent, and Circle maps. Experimental results demonstrate that the chaotic final processing significantly improves randomness properties and, in particular, that the Sinus map-based structure successfully passes all NIST tests.
subject: Articles
  topic: section
subject: LFSR
  topic: keywords
subject: Gold-SA II
  topic: keywords
subject: Chaotic maps
  topic: keywords
subject: Hybrid PRNG
  topic: keywords
subject: NIST SP 800-22
  topic: keywords
subject: Cryptography
  topic: keywords
subject: Cryptography
  topic: subjects
subject: Applied Mathematics
  topic: disciplines
creator: Eyüp Eröz
creator: Fatih Ozkaynak
creator: Erkan Tanyıldızı
rights: Copyright (c) 2026 https://creativecommons.org/licenses/by-nc/4.0/
date: 2026-01-31
publication date: 2026-01-31
starting page: 7
ending page: 15
doi: 10.69882/adba.chf.2026012

Cost-Effective Hardware Realization of Chaotic Systems via High-Performance STM32 DAC Interface
type: item
description: Chaotic systems play a crucial role in information security, cryptography, and secure communication systems due to their extreme sensitivity to initial conditions and inherent unpredictability. In this study, the dynamic behavior of the Scaled Zhongtang (SZ) chaotic system, which exhibits rich dynamical characteristics, is analyzed, and a low-cost, high-precision embedded system implementation using the STM32F429 microcontroller is presented. Within the scope of the study, the complexity of the SZ chaotic system is first validated through time series analysis, phase portraits, Lyapunov spectrum, and bifurcation analyses. Following the numerical analyses, the chaotic differential equation set is solved on the embedded system using the fourth-order Runge-Kutta (RK4) algorithm. The obtained chaotic data are converted into analog signals via the microcontroller’s internal 12-bit Digital-to-Analog Converter (DAC) without the need for an external hardware interface. The system performance is evaluated by comparing experimental data acquired from an oscilloscope with MATLAB simulation results. The comparison results demonstrate that the STM32-based implementation exhibits high consistency with theoretical models. This study proposes a flexible and cost-effective alternative for industrial applications of chaotic systems, addressing the stability issues of analog circuits and the high costs of FPGA-based systems.
subject: Articles
  topic: section
subject: Nonlinear dynamics
  topic: keywords
subject: Chaotic systems
  topic: keywords
subject: STM32 microcontroller
  topic: keywords
subject: Hardware realization
  topic: keywords
subject: Interface
  topic: keywords
subject: Embedded System
  topic: subjects
subject: Electronics and Computer Science
  topic: disciplines
creator: Selahattin Bulut
creator: Ihsan Pehlivan
creator: Burak Arıcıoğlu
rights: Copyright (c) 2026 https://creativecommons.org/licenses/by-nc/4.0/
date: 2026-01-31
publication date: 2026-01-31
starting page: 16
ending page: 20
doi: 10.69882/adba.chf.2026013

Ad-Click Prediction Enhanced by Nonlinear Dynamics-Inspired Feature Extraction and Ensemble Optimization
type: item
description: The primary objective of this study is to enhance the predictive performance of machine learning models used for estimating Click-Through Rate (CTR), a key metric in digital advertising analytics. Beginning with a baseline Logistic Regression (LR) model applied to the “Click-Through Rate Prediction” dataset from Kaggle, the study systematically incorporates multiple optimization layers to improve forecasting accuracy. Inspired by nonlinear dynamics concepts, new feature representations were derived from temporal patterns and textual fields using TF-IDF and Word2Vec-based embeddings. Hyperparameter optimization techniques were then applied to refine model behavior, followed by the construction of ensemble architectures combining LR, XGBoost, Random Forest (RF), and Support Vector Machine (SVM) classifiers. Experimental results show that the optimized ensemble achieved the highest F1-score of 0.8694, yielding an improvement of approximately 12.7% over the baseline model. Overall, the study provides a comprehensive examination of feature extraction strategies, model optimization procedures, and ensemble fusion techniques, demonstrating the clear advantage of hybrid approaches in complex CTR prediction tasks.
subject: Articles
  topic: section
subject: Feature extraction
  topic: keywords
subject: Ensemble learning
  topic: keywords
subject: Machine learning
  topic: keywords
subject: Hyperparameter optimization
  topic: keywords
subject: Classification
  topic: keywords
subject: Information Systems
  topic: disciplines
subject: Data Science
  topic: disciplines
creator: Ceyda Çağ
creator: Neslihan Akbulut
creator: Yusuf Çankırlı
rights: Copyright (c) 2026 https://creativecommons.org/licenses/by-nc/4.0/
date: 2026-01-31
publication date: 2026-01-31
starting page: 38
ending page: 46
doi: 10.69882/adba.chf.2026016

Nonlinear Dynamics and Chaos Control in a Discrete Sel'kov Model with Substrate Inhibition
type: item
description: An investigation of the dynamic effects of substrate inhibition in a modified Sel’kov model of glycolytic oscillations is presented in this paper. With a saturated nonlinear term in place of classical polynomial feedback, the discrete-time formulation captures enzymatic regulation more realistically. It exhibits complicated dynamics, including period-doubling bifurcations, compared to the classical continuous Sel’kov model, which undergoes Hopf bifurcation. In this study, the model’s behavior is investigated in multiple ways, including fixed point determination, stability assessment based on the Schur-Cohn criterion, and comprehensive numerical bifurcation analysis. Dynamic transitions from stability to periodic cycles, and then to chaos are revealed. Based on a comparative analysis with the classical model, we demonstrate how substrate inhibition induces complex nonlinear behavior through successive bifurcations. A deeper understanding of feedback regulation in biochemical systems can be gained from this study.
subject: Articles
  topic: section
subject: Discrete modified
  topic: keywords
subject: Sel’kov model
  topic: keywords
subject: Substrate inhibition
  topic: keywords
subject: Period-doubling bifurcation
  topic: keywords
subject: Chaos control
  topic: keywords
subject: Comparative dynamical analysis
  topic: keywords
subject: Chaos Theory and Control
  topic: subjects
subject: Control Systems Engineering
  topic: disciplines
creator: Ansar Abbas
creator: Abdul Khaliq
rights: Copyright (c) 2026 https://creativecommons.org/licenses/by-nc/4.0/
date: 2026-01-31
publication date: 2026-01-31
starting page: 29
ending page: 37
doi: 10.69882/adba.chf.2026015

Attack-Resistant Chaotic Communication System in Non-ideal Physical Channel
type: item
description: Coherent chaos-based communication is a developing technique for secure data transmission based on synchronization of chaotic oscillators at the transmitter and receiver sides, which is treated as a more secure method than non-coherent communication, chaotic symbolic dynamics, and other approaches. Nowadays, digital implementation of such systems allows high precision in parameter matching and sophisticated message recovery algorithms, though challenges remain: first, in adapting chaotic signals for non-ideal physical media, e.g., acoustic channels with frequency-dependent attenuation and noise, while, second, still providing the high level of security. The current study provides the implementation of a coherent chaotic communication system based on the Sprott Case S chaotic oscillator that meets these challenges. We utilize the modulation technique, minimizing changes in chaotic dynamics that may be captured by an intruder, propose an optimization of chaotic oscillator parameters to match channel characteristics and establish a signal normalization procedure to neutralize attenuation at the receiver side. Applying spectral and return map attacks, we show that the measures taken to counteract distortion in the path do not reduce the security of the transmission. In an experiment with a physical acoustic path, we demonstrate the practical operability of our approach.
subject: Articles
  topic: section
subject: Chaos-based communication
  topic: keywords
subject: Acoustic communication system
  topic: keywords
subject: Secure communications
  topic: keywords
subject: Chaotic shift keying
  topic: keywords
creator: Timur Karimov
creator: Alexander Mikhailov
creator: Vyacheslav Rybin
creator: Varvara Sheptunova
creator: Ivan Babkin
creator: Denis Butusov
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by-nc/4.0
date: 2025-07-30
publication date: 2025-07-30
starting page: 28
ending page: 37
doi: 10.69882/adba.chf.2025071

Partial Prey Migration as a Non-autonomous Harmonic Oscillator: Chaos-Order Transitions in a Forced Classical Lotka-Volterra Model
type: item
description: I investigate how partial prey migration cycles, analogous to a non-autonomous harmonic oscillator, force the classical Lotka-Volterra model and reshape predator-prey interactions. A 3D nonlinear system is introduced, into which the external forcing replicates the entry and exit of partial migrants from the ecosystem, devoid feedback loops. Numerical simulations reveal an elusive resilience contour of the species interplay under stationary migration cycles. Thus, quasi-periodic and chaotic fluctuations appear at a minimum migration magnitude, vanishing beyond a bifurcation-induced tipping point. However, resilient interactions surge in localized hotspots, i.e., narrow regions of phase space and forcing intensity. It is striking to note that the detected chaos exhibits a threefold complexity related to migration magnitude, initial conditions, and a functional response parameter, implying a basin of attraction intertwined at fractal boundaries. In contrast, the resilience non-monotonicity fades due to ascending cycles of partial prey migration involving recruitment of a cohort of migrants by its resident species. In this case, chaos is suppressed, leading to predictable oscillations and phase-locking. Even extreme predator-prey ratios (e.g., 10:1) do not endanger prey. Despite its parsimony, the framework offers a tractable prototype with broader ecological applicability for studying how exogenous forcings (e.g., climate-driven phenology), can alter ecosystems.
subject: Articles
  topic: section
subject: Nonautonomous oscillator
  topic: keywords
subject: Classical Lotka- Volterra model
  topic: keywords
subject: Partial migrationdriven dynamics
  topic: keywords
subject: Chaos-Order
  topic: keywords
subject: Resilience
  topic: keywords
creator: Safieddine Bouali
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by-nc/4.0
date: 2025-07-30
publication date: 2025-07-30
starting page: 50
ending page: 58
doi: 10.69882/adba.chf.2025074

Dynamical Analysis of Barium Titanate Crystal in Alternative Voltage RL Circuit
type: item
description: This brief paper theoretically investigates the dynamical characteristics of ferroelectric materials, specifically barium titanate $(BaTiO_3) $ crystal in alternative voltage resistor (R) and inductor (L) circuit. The theory of Landau-Ginzburg-Devonshire and Kirchhoff’s law are used to derive the equation for the polarization field in the $ BaTiO_3 $ crystal. The Averaging method is applied to obtain an approximate analytical solution, and the numerical simulations of the system’s equations is used to confirm the analytical obtained solution. The Melnikov method is used to investigate horseshoe chaos and the critical amplitude of excitation. The phase portraits, Poincaré sections, local maxima and greatest Lyapunov exponent are drawn to confirm the results obtained with Melnikov method.
subject: Articles
  topic: section
subject: Barium titanate crystal
  topic: keywords
subject: Polarization
  topic: keywords
subject: Averaging method
  topic: keywords
subject: Melnikov method
  topic: keywords
subject: Horseshoe chaos
  topic: keywords
creator: Guy Joseph Eyebe
creator: Justin Mibaile
creator: Rolande Tsapla Fotsa
creator: Gambo Betchewe
creator: Alidou Mohamadou
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by-nc/4.0
date: 2025-07-30
publication date: 2025-07-30
starting page: 38
ending page: 42
doi: 10.69882/adba.chf.2025072

A Study on Hindmarsh-Rose Neurons Under an Electric Field
type: item
description: Today, we are at the heart of a great revolution brought about by emerging new ideas of chaos. The discovery of chaos has had a major impact on many fields of science, engineering, and mathematics. This phenomenon sheds new light on explaining the workings of the Earth’s weather system, lasers, fluids, mechanical structures, earthquakes, etc. Understanding the brain and its behavior has been an active research field with various applications, including finding new solutions to cure brain diseases, designing better robots, and studying the behavior of neural networks. So far, various neural models have been developed. One such model is the Hindmarsh-Rose biological neuron model, which mimics the thalamic neurons of the brain. In this study, we analyzed the behavior of the Hindmarsh-Rose neurons under an electric field with a certain parameter. The Hindmarsh-Rose neuron model used here enables us to simulate how neurons behave in various situations, such as when they are exposed to electric fields. A program developed in MATLAB was used to perform simulations. Time response plots were obtained by varying parameters influencing the Hindmarsh-Rose neuron model. In this article, we look at how these factors change the way neurons act. Sometimes, they go from a steady firing pattern to more complex behavior, like oscillation death, which is shown by the simulations done in MATLAB software. From this article, one can understand how to improve a neural network for artificial intelligence. Additionally, how different external stimuli affect brain activity, which can lead to various neurological disorders.
subject: Articles
  topic: section
subject: Hindmarsh–Rose neuron model
  topic: keywords
subject: Membrane potential
  topic: keywords
subject: Synchronization
  topic: keywords
subject: Quiescent
  topic: keywords
subject: Coupled system
  topic: keywords
subject: Nonlinear Dynamics
  topic: subjects
subject: Applied Mathematics; Nonlinear Dynamics; Dynamical Systems; Mathematical Modeling; Chaos Theory
  topic: disciplines
creator: Vineetha Erathara Pious
creator: Stella Kooliath Antony
rights: Copyright (c) 2026 https://creativecommons.org/licenses/by-nc/4.0
date: 2026-01-31
publication date: 2026-01-31
starting page: 1
ending page: 6
doi: 10.69882/adba.chf.2026011

Synergistic Construction of High-Performance S-Boxes based on Chaotic Systems: A Paradigm Shift in Cryptographic Security Design
type: item
description: Exchange of information between two nodes is a big issue in intenet these days. Multiple cryptosystems employed for this porpose with various mathmatical approaches. Most of these approaches uitilize subsitutions and pemutations. The subsituation S-box is a look up table that exchange x bits input with y bits output is incharge of substitution approach. The build of S-box with stong cryptographic power is important in recent cryptosystems. In this paper a novel approach for building roboust and dynamic S-box with compound multi-dimentional chaotic systems. Lorenze and henon maps employed for construction of strong S-Box with multiple security performance metrics :non-linearity(NL), Strict Avalanche Criterion (SAC), Bit-Independence Criterion (BIC), Linear-Probability (LP) and differential-Probability (LP).The results showed that proposed S_box is will be powerfull for modern cryptosystems.
subject: Articles
  topic: section
subject: Cryptography
  topic: keywords
subject: S-box
  topic: keywords
subject: Security
  topic: keywords
subject: Chaotic map
  topic: keywords
subject: Nonlinearity
  topic: keywords
creator: Zaid Abdulsattar Abdulrazaq
creator: Harith Ghanim Ayoub
creator: Hakam Zaidan
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by-nc/4.0
date: 2025-07-30
publication date: 2025-07-30
starting page: 43
ending page: 49
doi: 10.69882/adba.chf.2025073

A Two-Memristor-based Chaotic System with Symmetric Bifurcation and Multistability
type: item
description: In this work, the study of an innovative chaotic system made from two memristors with symmetric bifurcation and multistability is presented. Within a four dimensional chaotic framework, the system is architected with two flux controlled memristors. Computational simulations reveal intricate dynamical phenomena such as symmetric bifurcations, multistability, and very large sensitivity to initial conditions. Using Lyapunov exponents, bifurcation diagrams and phase portraits, we investigate the system's ability to produce chaotic attractors of pronounced multistability. Pinched hysteresis loop and system offset investigation at different frequencies are investigated for possible applications in neuromorphic computing, random number generation and secure communication protocols. We further advance our understanding of the complex dynamical properties of memristive chaotic systems. A representative analog circuit corroborates their numerical findings.
subject: Articles
  topic: section
subject: Multistability
  topic: keywords
subject: Analog circuit
  topic: keywords
subject: Chaotic systems
  topic: keywords
subject: Bifurcation
  topic: keywords
creator: Awais Khan
creator: Chunbiao Li
creator: Xin Zhang
creator: Xiaoliang Cen
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by-nc/4.0/
date: 2025-01-31
publication date: 2025-01-31
starting page: 1
ending page: 7
doi: 10.69882/adba.chf.2025011

Permanent Magnet Synchronous Motor with Load Torque: Dynamics, Circuitry Execution and Control
type: item
description: This paper is interested in the study of the dynamics and control of the permanent magnet synchronous motor with load torque (PMSMLT). PMSMLT has three fixed points where one is saddle and the two others are saddle focus. PMSMLT exhibits no oscillations, periodic characteristics, chaotic characteristics and coexistence between no oscillations and chaotic characteristics. In order to validate the results obtained numerically, an electronic implementation of PMSMLT is performed in probe simulation program with integrated circuit emphases (PSPICE) environment which reveals a concordance between the numerical simulations and the experimental verifications. The coexisting characteristics is eliminated by the linear augmentation control method.
subject: Articles
  topic: section
subject: Permanent magnet synchronous motor
  topic: keywords
subject: Load torque
  topic: keywords
subject: Chaos
  topic: keywords
subject: Coexisting characteristics
  topic: keywords
subject: Linear augmentation control
  topic: keywords
subject: Implementation circuit
  topic: keywords
creator: Rolande Tsapla Fotsa
creator: Paloma Kevina Koubeu Papemsi
creator: Gideon Pagnol Ayemtsa Kuete
creator: Justin Roger Mboupda Pone
creator: Serge Raoul Dzonde Naoussi
creator: Foutse Momo
creator: Pierre Ele
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by-nc/4.0/
date: 2025-01-31
publication date: 2025-01-31
starting page: 14
ending page: 19
doi: 10.69882/adba.chf.2025013

FPGA-Based Chaotic Oscillator Designs and Performance Analysis
type: item
description: Chaotic systems are highly sensitive to initial conditions, where even minute changes can result in vastly different outcomes. The non-linear nature of chaotic systems prevents them from reaching a stable state, instead exhibiting continuous change. This inherent unpredictability makes chaotic systems particularly valuable in fields such as cryptography, random number generation, and secure communications, where the need for complex and difficult-to-predict patterns is crucial. FPGA chips allow for hardware-level customization, enabling the optimization of chaotic systems for specific tasks. Implementing chaotic oscillators and systems on FPGA platforms facilitates efficient solutions for security-related applications, including encryption, pseudorandom number generation, and secure communication protocols. Additionally, the high-speed performance, low power consumption, and parallel processing capabilities of FPGAs make them ideal for implementing chaotic systems in industrial and commercial applications, where efficiency and security are paramount. One of the most basic structures used in real time chaos-based applications is chaotic oscillators. In this study, FPGA based chaotic oscillators presented in the literature have been examined according to important parameters such as maximum operating frequency of the designed system, chaotic oscillator type, application area and numerical methods used for designs and the results have been discussed.
subject: Articles
  topic: section
subject: Chaos
  topic: keywords
subject: Chaotic oscillators
  topic: keywords
subject: FPGA
  topic: keywords
subject: Maximum operating frequency
  topic: keywords
subject: Numerical methods
  topic: keywords
creator: Muhammed Furkan Taşdemir
creator: Murat Tuna
creator: Ismail Koyuncu
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by-nc/4.0/
date: 2025-01-31
publication date: 2025-01-31
starting page: 8
ending page: 13
doi: 10.69882/adba.chf.2025012

Investigation of the Impact of Alloying Elements on the Mechanical Properties of Superalloys Using Explainable Artificial Intelligence
type: item
description: This study investigates the impact of alloying elements on the mechanical properties of Ni-Cr-Fe-based superalloys using a computational materials science approach. Fifty different compositions of superalloys, commonly known as Inconel and Incoloy, were modeled using the JMatPro software. The mechanical properties, including 0.2% proof stress (MPa), fracture stress (MPa), and Young’s modulus (GPa), were simulated across a temperature range from 540°C to 920°C at 20°C intervals for each alloy. The simulation generated a comprehensive dataset comprising 1000 rows. This dataset was then utilized to train an explainable artificial intelligence (XAI) model, leveraging advanced techniques such as SHAP (SHapley Additive exPlanations), LIME (Local Interpretable Model-agnostic Explanations), and Partial Dependence Plots (PDP). The dataset was analyzed using an XAI-based regression model employing the XGBoost algorithm. The interpretability graphs were analyzed to evaluate the individual contributions of each alloying element to the mechanical properties over the entire temperature range. The findings provide detailed insights into the positive or negative effects of alloying elements, enabling a better understanding of their role in optimizing superalloy performance under various thermal conditions. This work highlights the potential of integrating computational materials modeling and explainable AI to advance the design and development of high-performance materials.
subject: Articles
  topic: section
subject: Explainable artificial intelligence
  topic: keywords
subject: Computational materials
  topic: keywords
subject: Superalloys mechanical properties
  topic: keywords
creator: Berkay Emin
creator: Yusuf Uzunoğlu
creator: Yusuf Alaca
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by-nc/4.0/
date: 2025-01-31
publication date: 2025-01-31
starting page: 20
ending page: 27
doi: 10.69882/adba.chf.2025014

A Novel Chaos-Based Encryption Technique with Parallel Processing Using CUDA for Mobile Powerful GPU Control Center
type: item
description: Chaotic systems possess unique properties that can be leveraged for cybersecurity. These properties stem from the complex and unpredictable nature of images, which makes it challenging for systems to interpret them. When combined with CUDA, chaotic systems benefit from high-efficiency parallel processing capabilities, allowing for the rapid and secure handling of large data sets. Therefore, chaotic systems can be effectively used to securely store and conceal images. In this study, a CUDA-supported chaos-based parallel processing encryption mechanism for mobile control centers is developed. Encryption processes leverage the powerful GPU of the control center. This allows for the fast encryption and decryption of image data received from multiple devices connected to the control center via wired or wireless connections. For encryption, the Logistic Map is used to generate random numbers. Using this map, image data is subjected to XOR operations, encrypting the R, G, B, and Gray Scale channels of the images. Initially, an analysis of the numbers generated from this map is conducted, followed by a detailed explanation of the encryption technique. The technique is then applied to image data, and image analyses are performed. Finally, the performance of the encryption technique is compared with other studies, and encryption speeds are examined. The results show that the new encryption technique provides significantly fast encryption and security levels comparable to other studies. The key discovery of this research is that the devised mechanism is well-suited for parallel processing, allowing for rapid image encryption using the proposed method. For encrypting large IoT files, random number generation is initially performed, followed by statistical tests. Subsequently, encryption is executed using the developed algorithm, and security analyses are conducted. The performance of the proposed mechanism is compared with other studies in the literature, and the results from i…
subject: Articles
  topic: section
subject: Chaos-based encryption
  topic: keywords
subject: CUDA programming
  topic: keywords
subject: Logistic map
  topic: keywords
subject: Image encryption
  topic: keywords
subject: Internet of things
  topic: keywords
creator: Harun Emre Kıran
rights: Copyright (c) 2024 https://creativecommons.org/licenses/by-nc/4.0
date: 2024-07-31
publication date: 2024-07-31
starting page: 6
ending page: 18
doi: 10.69882/adba.chf.2024072

Digital Implementation of Chaotic Systems Using Nvidia Jetson AGX Orin and Custom DAC Converter
type: item
description: Digital implementation of chaotic systems has many advantages. Chaotic systems realized on digital platforms offer higher flexibility and computational accuracy compared to traditional analog systems. This flexibility and accuracy are of great importance for engineering applications. Furthermore, digital solutions are usually more cost-effective, which is a great economic advantage. In this study, Nvidia Jetson AGX Orin board and 16-bit converter board are used for digital realization of chaotic systems. The Nvidia Jetson AGX Orin is a platform that stands out with its high processing power and energy efficiency. The 16-bit converter card stands out with its sensitive data processing capacity. Thanks to this technological infrastructure, chaotic system equations can be successfully solved in a digital environment and more advanced, flexible, reliable and cost-effective solutions are obtained. These solutions provide significant advantages in various applications in engineering. In particular, the use of digital chaotic systems in areas such as modeling, simulation and control of complex systems offers more efficient and effective results than traditional methods. Digital platforms also facilitate parametric investigations and optimization processes of chaotic systems, enabling more in-depth analysis.
subject: Articles
  topic: section
subject: Chaotic system
  topic: keywords
subject: Nvidia Jetson
  topic: keywords
subject: AGX Orin
  topic: keywords
subject: Digital analog converter
  topic: keywords
subject: Oscilloscope
  topic: keywords
subject: Chaotic System
  topic: subjects
subject: Nvidia Jetson AGX Orin
  topic: subjects
subject: Digital Analog Converter
  topic: subjects
subject: Oscilloscope
  topic: subjects
subject: Electronics and Computer Science
  topic: disciplines
creator: Berkay Emin
creator: Mustafa Yaz
rights: Copyright (c) 2024 https://creativecommons.org/licenses/by-nc/4.0
date: 2024-07-31
publication date: 2024-07-31
starting page: 38
ending page: 41
doi: 10.69882/adba.chf.2024075

Numerical Exploration of a Network of Nonlocally Coupled Josephson Junction Spurred by Wien Bridge Oscillators
type: item
description: This paper is devoted to the numerical investigation of the collective dynamics of nonlocally coupled Josephson junctions (JJ) spurred by Wien bridge oscillators (JJSWBOs). A single JJSWBO displays monostable and bistable chaotic characteristics, bistable period-3-oscillations and coexistence between regular and chaotic characteristics. In order to investigate the collective dynamics of the considered network, the local dynamics is set in the bistable regime which includes periodic and chaotic dynamics. The initial conditions for the network dynamics are specially prepared such that the networks units are randomly distributed on these two types of dynamical behaviors. As the value of the coupling strength increases, the dynamics of the network of JJSWBOs undergoes a transition from complete incoherence to coherent travelling waves via a chimera state.
subject: Articles
  topic: section
subject: Josephson junction
  topic: keywords
subject: Wien bridge oscillator
  topic: keywords
subject: Chaotic and coexisting characteristics
  topic: keywords
subject: Nonlocal coupling
  topic: keywords
subject: Coherent and incoherent behaviors
  topic: keywords
subject: Chimera state
  topic: keywords
subject: keywords
  topic: subjects
creator: Dianorré Tokoue Ngatcha
creator: Buris Peggy Ndemanou
creator: Alain Francis Talla
creator: Serge Gervais Ngueuteu Mbouna
creator: Sifeu Takougang Kingni
rights: Copyright (c) 2024 https://creativecommons.org/licenses/by-nc/4.0
date: 2024-07-31
publication date: 2024-07-31
starting page: 1
ending page: 5
doi: 10.69882/adba.chf.2024071

Comparative Analysis of State-of-the-Art Q&A Models: BERT, RoBERTa, DistilBERT, and ALBERT on SQuAD v2 Dataset
type: item
description: In the rapidly evolving landscape of natural language processing (NLP) and artificial intelligence, recent years have witnessed significant advancements, particularly in text-based question-answering (QA) systems. The Stanford Question Answering Dataset (SQuAD v2) has emerged as a prominent benchmark, offering diverse language understanding challenges. This study conducts a thorough examination of cutting-edge QA models—BERT, DistilBERT, RoBERTa, and ALBERT—each featuring distinct architectures, focusing on their training and performance on SQuAD v2.The analysis aims to uncover the unique strengths of each model, providing insights into their capabilities and exploring the impact of different training techniques on their performance. The primary objective is to enhance our understanding of text-based QA systems' evolution and their effectiveness in real-world scenarios. The results of this comparative study are poised to influence the utilization and development of these models in both industry and research.The investigation meticulously evaluates BERT, ALBERT, RoBERTa, and DistilBERT QA models using the SQuAD v2 dataset, emphasizing instances of accurate responses and identifying areas where completeness may be lacking. This nuanced exploration contributes to the ongoing discourse on the advancement of text-based question-answering systems, shedding light on the strengths and limitations of each QA model.Based on the results obtained, ALBERT achieved an exact match of 86.85% and an F1 score of 89.91% on the SQuAD v2 dataset, demonstrating superior performance in both answerable ('HasAns') and unanswerable ('NoAns') questions. BERT and RoBERTa also showed strong performance, while DistilBERT lagged slightly behind. This study provides a significant contribution to the advancement of text-based question-answering systems, offering insights that can shape the utilization of these models in both industry and research domains.
subject: Articles
  topic: section
subject: Question- Answering models BERT
  topic: keywords
subject: RoBERTa
  topic: keywords
subject: DistilBERT
  topic: keywords
subject: ALBERT
  topic: keywords
subject: SQuAD v2 Dataset
  topic: keywords
subject: Model performance
  topic: keywords
subject: Question-Answering Models
  topic: subjects
subject: BERT
  topic: subjects
subject: RoBERTa
  topic: subjects
subject: DistilBERT
  topic: subjects
subject: ALBERT
  topic: subjects
subject: SQuAD v2 Dataset
  topic: subjects
subject: Model Performance
  topic: subjects
creator: Cem Özkurt
rights: Copyright (c) 2024 https://creativecommons.org/licenses/by-nc/4.0
date: 2024-07-31
publication date: 2024-07-31
starting page: 19
ending page: 30
doi: 10.69882/adba.chf.2024073

Analysis of a Resistive-Capacitive Shunted Josephson Junction with Topologically Nontrivial Barrier Coupled to a RLC Resonator
type: item
description: This paper presents the resistive-capacitive shunted Josephson junction (RCSJJ) with a topologically nontrivial barrier (TNB) coupled to a linear RLC resonator. The rate equations describing RCSJJ with TNB coupled to the linear RLC resonator are established via Kirchhoff’s current and voltage laws. The model exhibits four, two, or no equilibrium points depending on the external direct current (DC) source and the fractional parameter. The stability analysis of the equilibrium points with credit to the Routh-Hurwitz stability criterion reveals that the stability of equilibrium points depends on the DC source and the fractional parameter. Current-voltage characteristic reveals the presence of a birhythmicity zone which is sensitive to the fractional parameter m. As the fractional parameter increases, the coexistence of the resonant state is destroyed, which is followed simultaneously by the appearance of a new resonance state. Depending on initial conditions, birhythmic behaviour is characterized by the existence of a limit cycle. The projection of the phase space in the specific plane and the time evolution of charge is predicted in which the amplitude of attractors reported is sensitive to the parameter m. Lastly, with a defined fractional parameter, the amplitude of the branch locked to the resonator is greater than the unlocked branch.
subject: Articles
  topic: section
subject: Josephson junction
  topic: keywords
subject: Topologically nontrivial barrier
  topic: keywords
subject: RLC resonator
  topic: keywords
subject: Birhythmic zone
  topic: keywords
subject: Limit cycle
  topic: keywords
subject: Resonant state
  topic: keywords
subject: dynamic systems
  topic: subjects
subject: control
  topic: subjects
creator: Jules Metsebo
creator: Boubakary Abdou
creator: Dianorré Tokoue Ngatcha
creator: Isidore Komofor Ngongiah
creator: Paul Didier Kamdem Kuate
creator: Justin Roger Mboupda Pone
rights: Copyright (c) 2024 https://creativecommons.org/licenses/by-nc/4.0
date: 2024-07-31
publication date: 2024-07-31
starting page: 31
ending page: 37
doi: 10.69882/adba.chf.2024074