Eur. Phys. J. Spec. Top. (2021) 230: 3369-3379
https://doi.org/10.1140/epjs/s11734-021-00115-y

Regular Article

Effects of noise on the wave propagation in an excitable media with magnetic induction

¹ Center for Nonlinear Systems, Chennai Institute of Technology, Chennai, India
² Mathematical Institute, University of Oxford, Andrew Wiles Building, Oxford, UK
³ Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science and Technology, 210044, Nanjing, China
⁴ Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science and Technology, Nanjing, China
⁵ Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

^d anitha.karthikeyan@tdtu.edu.vn

Received: 13 January 2021
Accepted: 15 April 2021
Published online: 22 April 2021

Abstract

In this paper, we investigate the wave propagation phenomenon and network dynamics of an improved Hindmarsh–Rose neuron model considered with magnetic induction. The dynamical properties of the improved neuron model in discussed with the help of eigenvalues, Lyapunov exponents and bifurcation plots. A simple comparison between the exponential flux model and quadratic flux model is investigated and shown that the exponential flux model could show behavior like the quadratic model with its memductance monotonically increasing or decreasing depending on the polarity of the voltage. In the network dynamics investigation, we have considered two additional external disturbances such as the noise and flux excitation. A mathematical model of a lattice array with Box–Mueller type random noise and a sinusoidal periodic flux excitation is defined. The wave propagation phenomenon in the presence of noise is investigated using the noise variance as the control parameter. We could show that when the noise is applied to the network for the entire simulation time, the spiral waves are effectively suppressed for very low noise variance values.