Keywords
Wien bridge oscillator
Chaotic and coexisting characteristics
Nonlocal coupling
Coherent and incoherent behaviors
Chimera state
How to Cite
Abstract
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.
References
Abrams, D. M. and S. H. Strogatz, 2004 Chimera states for coupled oscillators. Physical Review Letters 93: 174102.
Dudkowski, D., Y. Maistrenko, and T. Kapitaniak, 2016 Occurrence and stability of chimera states in coupled externally excited oscillators. Chaos 26: 116306.
Filatrella, G., G. Rotoli, N. Grønbech-Jensen, R. D. Parmentier, and N. F. Pedersen, 1992 Model studies of long josephson junction arrays coupled to a high-q resonator. Journal of Applied Physics 72: 3179–3185.
Gopal, R., V. K. Chandrasekar, D. V. Senthilkumar, A. Venkatesan, and M. Lakshmanan, 2018 Chimera at the phase-flip transition of an ensemble of identical nonlinear oscillators. Communications in Nonlinear Science and Numerical Simulation 59: 30–46.
Hagerstrom, A. M., T. E. Murphy, R. Roy, P. Hövel, I. Omelchenko, et al., 2012 Experimental observation of chimeras in coupled-map lattices. Nature Physics 8: 658–661.
Kuramoto, Y. and D. Battogtokh, 2002 Coexistence of coherence and incoherence in nonlocally coupled phase oscillators. Nonlinear Phenomena in Complex Systems 5: 380–385.
Lei, Z., S. Pu, H. Zhang, C. Yao, Y. Qian, et al., 2022 Bistability-induced chimeras in one-dimensional paced excitable ring with nonlocal couplings. Europhysics Letters 139: 62001.
Mishra, A., C. Hens, M. Bose, P. K. Roy, and S. K. Dana, 2015 Chimeralike states in a network of oscillators under attractive and repulsive global coupling. Physical Review E 92: 062920.
Mishra, A., S. Saha, P. K. Roy, M. Bose, P. Louodop, et al., 2017a Coherent libration to coherent rotational dynamics via chimeralike states and clustering in a josephson junction array. Physical Review E 95: 010201(R).
Mishra, A., S. Saha, P. K. Roy, T. Kapitaniak, and S. K. Dana, 2017b Multicluster oscillation death and chimeralike states in globally coupled josephson junctions. Chaos 27: 023110.
Nganso, E. N., S. G. N. Mbouna, R. Yamapi, G. Filatrella, and J. Kurths, 2023 Two-attractor chimera and solitary states in a network of nonlocally coupled birhythmic van der pol oscillators. Chaos, Solitons and Fractals 169: 113235.
Ngongiah, I., B. Ramakrishnan, G. Kuiate, A. Akgül, and B. Nana, 2023 Mechanical arm(s) driven by josephson junction circuit(s), mimicking the movement pattern of myriapods. Physica Scripta 98: 045221.
Omelchenko, I., O. E. Omel’chenko, P. Hövel, and E. Schöll, 2013 When nonlocal coupling between oscillators becomes stronger: patched synchrony or multichimera states. Physical Review Letters 110: 224101.
Parastesh, F., S. Jafari, H. Azarnoush, Z. Shahriari, Z.Wang, et al., 2021 Chimeras. Physics Reports 898: 1–114.
Pikovsky, A., M. Rosenblum, and J. Kurths, 2001 Synchronization: A Universal Concept in Nonlinear Science. Cambridge University Press, Cambridge, UK.
Ramakrishnan, B., L. Tabejieu, I. Ngongiah, S. Kingni, R. Siewe, et al., 2021 Suppressing chaos in josephson junction model with coexisting attractors and investigating its collective behavior in a network. Journal of Superconductivity and Novel Magnetism 34: 2761–2769.
Ramamoorthy, R., Z. Shahriari, H. Natiq, K. Rajagopal, and C. Li, 2022 Chimera states in coupled memristive chaotic systems: effects of control parameters. Europhysics Letters 139: 41001.
Rybalova, E., V. S. Anishchenko, G. I. Strelkova, and A. Zakharova, 2019 Solitary states and solitary state chimera in neural networks. Chaos 29: 071106.
Schöll, E., 2016 Synchronization patterns and chimera states in complex networks: interplay of topology and dynamics. The European Physical Journal Special Topics 225: 891–919.
Shepelev, I. A., T. E. Vadivasova, A. V. Bukh, G. I. Strelkova, and V. S. Anishchenko, 2017 New type of chimera structures in a ring of bistable fitzhugh–nagumo oscillators with nonlocal interaction. Physics Letters A 381: 1398–1404.
Sriram, B., D. Godonou, C. Ainamon, I. Ngongiah, and K. Rajagopal, 2023 Analysis and microncontroller implementation of josephson junction driven by wien bridge oscillator. Physica Scripta 98: 045213.
Tinsley, M. R., S. Nkomo, and K. Showalter, 2012 Chimera and phase-cluster states in populations of coupled chemical oscillators. Nature Physics 8: 662–665.
Yeldesbay, A., A. Pikovsky, and M. Rosenblum, 2014 Chimeralike states in an ensemble of globally coupled oscillators. Physical Review Letters 112: 144103.
Zakharova, A., 2020 Chimera Patterns in Networks: Interplay between Dynamics, Structure, Noise, and Delay. Springer Nature Switzerland AG, Cham.
Zhang, H., Z. Chen, F. Liu, Z. Lei, Z. Zheng, et al., 2024 Alternate attractor chimeralike states on rings of chaotic lorenz-type oscillators. New Journal of Physics 26: 023016.
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