Chaotic synchronization of time-delay coupled Hindmarsh-Rose neurons via nonlinear control

摘要

Chaotic synchronization of two time-delay coupled Hindmarsh-Rose neurons via nonlinear control is investigated in this paper. Both the intrinsic slow current delay in a single Hindmarsh-Rose neuron and the coupling delay between the two neurons are considered. When there is no control, chaotic synchronization occurs for a limited range of the coupling strength and the time-delay values. To obtain complete chaotic synchronization irrespective of the time-delay or the coupling strength, we propose two nonlinear control schemes. The first uses adaptive control for chaotic synchronization of two electrically coupled delayed Hindmarsh-Rose neuron models. The second derives the sufficient conditions to ensure a complete synchronization between master and slave models through appropriate Lyapunov-Krasovskii functionals and the linear matrix inequality technique. Numerical simulations are carried out to show the effectiveness of the proposed methods.