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Hettiarachchi, Imali T.; Lakshmanan, S.; Bhatti, Asim; Lim, C. P.; Prakash, M.; Balasubramaniam, P.; Nahavandi, Saeid

Chaotic synchronization of time-delay coupled Hindmarsh-Rose neurons via nonlinear control. (English) Zbl 1349.34246

Nonlinear Dyn. 86, No. 2, 1249-1262 (2016).
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.

Cited in 10 Documents

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 inequality
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References:

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