Lyapunov-based synchronization of two coupled chaotic Hindmarsh-Rose neurons

Abstract

Abstract.This paper addresses the synchronization of coupled chaotic Hindmarsh-Rose neurons. A sufficient condition for self-synchronization is first attained by using Lyapunov method. Also, to achieve the synchronization between two coupled Hindmarsh-Rose neurons when the selfsynchronization condition not satisfied, a Lyapunov-based nonlinear control law is proposed and its asymptotic stability is proved. To verify the effectiveness of the proposed method, numerical simulations are performed.

Random attractor for stochastic Hindmarsh-Rose equations with multiplicative noise

“…2, (f) the x-z phase portrait when J = 3.1. Source: [25] Neuronal signals are short electrical pulses called spike or action potential. Neurons often exhibit bursts of alternating phases of rapid firing spikes and then quiescence.…”

“…Time responses of the membrane potential for various value of the stimulated current: (a) resting state when J = 0, (b) tonic spiking when J = 1.2, (c) regular bursting when J = 2.2, (d) chaotic bursting when J = 3.1, (e) the x-z phase portrait when J = 2.2, (f) the x-z phase portrait when J = 3.1. Source: [25] Neuronal signals are short electrical pulses called spike or action potential. Neurons often exhibit bursts of alternating phases of rapid firing spikes and then quiescence.…”