A Study on Hindmarsh-Rose Neurons Under an Electric Field
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Keywords

Hindmarsh–Rose neuron model
Membrane potential
Synchronization
Quiescent
Coupled system

How to Cite

A Study on Hindmarsh-Rose Neurons Under an Electric Field. (2026). Chaos and Fractals, 3(1), 1-6. https://doi.org/10.69882/adba.chf.2026011

Abstract

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.

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References

Baker, G. and J. Gollub, 1996. Chaotic Dynamics: An Introduction. Cambridge University Press.

Boccaletti, S., J. Kurths, G. Osipov, D. Valladares, and C. Zhou, 2002. The synchronization of chaotic systems. Physics Reports, 366: 1–101.

Coombes, S., P. Bressloff (eds.), 2005. Bursting: The Genesis of Rhythm in the Nervous System. World Scientific.

Gerstner, W., W. M. Kistler, 2002. Spiking Neuron Models: Single Neurons, Populations, Plasticity. Cambridge University Press.

Hilborn, R. C., 2000. Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers. Oxford University Press.

Hindmarsh, J. and R. Rose, 1982. A model of the nerve impulse using two first-order differential equations. Nature, 296: 162–164.

Hindmarsh, J. and R. Rose, 1984. A model of neuronal bursting using three coupled first-order differential equations. Proc. R. Soc. Lond. B Biol. Sci., 221: 87–102.

Hodgkin, A. and A. Huxley, 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology, 117: 500–544.

Izhikevich, E., 2007. Dynamical Systems in Neuroscience. MIT Press.

Lange, E., 2006. Neuron models of the generic bifurcation type: network analysis and data modeling.

Ma, J., G. Zhang, T. Hayat, et al., 2018. Model electrical activity of neuron under electric field. Nonlinear Dynamics, 95: 1585–1598.

Mustafa, M., W. K. Putra, and K. Agus, 2013. Development of dynamics and synchronization model for coupled neurons using Hindmarsh–Rose model. Applied Mathematical Sciences, 7: 135–152.

Pyragas, K., 1996. Weak and strong synchronization of chaos. Physical Review E, 54: R4508–R4511.

Resmi, V., G. Ambika, and R. E. Amritkar, 2011. General mechanism for amplitude death in coupled systems. Physical Review E, 84: 046212.

Storace, M., D. Linaro, and E. de Lange, 2008. The Hindmarsh–Rose neuron model: Bifurcation analysis and piecewise-linear approximations. Chaos, 18: 033128.

Thottil, S. K. and R. P. Ignatius, 2019. Influence of memristor and noise on H–R neurons. Nonlinear Dynamics, 95: 239–257.

Walleczek, J., 2000. Self-Organized Biological Dynamics and Nonlinear Control: Toward Understanding Complexity, Chaos and Emergent Function in Living Systems. Cambridge University Press.

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