Eur. Phys. J. Special Topics 229, 929-942 (2020)
https://doi.org/10.1140/epjst/e2020-900247-7

Regular Article

Route to hyperchaos and chimera states in a network of modified Hindmarsh-Rose neuron model with electromagnetic flux and external excitation

¹ College of Electrical and Information Engineering, Shaoyang University, Shaoyang 422000, P.R. China
² School of Physics and Electronics, Central South University, Changsha 410083, P.R. China
³ Center for Nonlinear Dynamics, Institute of Research and Development, Defence University, Bishoftu, Ethiopia

^a email: heshaobo_123@163.com

Received: 31 October 2019
Received in final form: 26 November 2019
Published online: 26 March 2020

Abstract

Analyzing the chaos and bursting phenomenon of neurons has been of interest in the past decade. In this paper, we discuss an extended Hindmarsh-Rose neuron model by taking into consideration the slowly interacting cell phenomenon due to the calcium ions. In the extended model, we consider the effect of an external forcing current, and the electromagnetic coupling between the magnetic flux and the membrane potential of the neuron. We analyze the modified neuron model in the presence of periodic and quasi-periodic excitations. A more complex chaotic behavior (hyperchaos) is identified in the neuron model. The results also demonstrate the multistable nature, which was not explored earlier. To discuss the dynamical behavior of the modified neuron in a network, we construct a ring network of neurons and capture the spatiotemporal patterns of the neuron in the network, in the presence of different excitations.