Title: Simple synchronisation scheme of chaotic Chua's systems with cubic nonlinearity in complex coupled networks

Authors: Himesh Handa; B.B. Sharma

Addresses: Department of Electrical Engineering, National Institute of Technology, Hamirpur, Himachal Pradesh 177005, India ' Department of Electrical Engineering, National Institute of Technology, Hamirpur, Himachal Pradesh 177005, India

Abstract: In this paper, the problem of synchronisation of a complex coupled chaotic network is addressed. Generally Lyapunov theory-based controller design techniques are rigorously used but contraction theory-based results are significantly different from those of their Lyapunov-based counterparts. The proposed approach provides a very simple way of establishing convergence of the corresponding states of different systems which are part of a coupled network. For achieving this objective, a virtual system is designed suitably for the given network, which helps in establishing the results in an indirect way. In order to ensure synchronisation the coupling strengths between the coupled systems are properly chosen so as to ensure the contracting nature of the virtual system. As a particular case, a synchronisation problem of a network of chaotic Chua's systems with cubic nonlinearity is explored. Bidirectional coupling is assumed between the systems and the case of all-to-all coupling between all the nodes of the network is considered. Numerical simulations are presented in the end to verify the effectiveness of the proposed approach.

Keywords: chaotic systems; synchronisation; contraction theory; virtual systems; complex coupled networks; cubic nonlinearity; convergence; chaos; numerical simulation.

DOI: 10.1504/IJANS.2014.068255

International Journal of Applied Nonlinear Science, 2014 Vol.1 No.4, pp.300 - 311

Received: 04 Sep 2013
Accepted: 18 Jun 2014
Published online: 08 Apr 2015 *

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