Chaotic synchronization of time-delay coupled Hindmarsh-Rose neurons via nonlinear control. (English) Zbl 1349.34246
Summary: 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.
MSC:
34H10 | Chaos control for problems involving ordinary differential equations |
37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
90C25 | Convex programming |
34D06 | Synchronization of solutions to ordinary differential equations |
93C10 | Nonlinear systems in control theory |
34B45 | Boundary value problems on graphs and networks for ordinary differential equations |
Keywords:
Hindmarsh-Rose neuron; chaotic synchronization; nonlinear control; linear matrix inequalityReferences:
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