Title: Hyperchaos, qualitative analysis, control and synchronisation of a ten-term 4-D hyperchaotic system with an exponential nonlinearity and three quadratic nonlinearities

Authors: Sundarapandian Vaidyanathan

Addresses: Research and Development Centre, Vel Tech University, Avadi, Chennai – 600 062, Tamil Nadu, India

Abstract: In this research work, a ten-term novel hyperchaotic system with an exponential nonlinearity and three quadratic nonlinearities has been derived. The Lyapunov exponents of the hyperchaotic system are obtained as L₁ = 14.21985, L₂ = 0.04417, L₃ = 0 and L₄ = −36.82311. Since the maximal Lyapunov exponent (MLE) of the novel hyperchaotic system is L₁ = 14.21985, which is a large value, the novel hyperchaotic system exhibits strong chaotic behaviour. The Kaplan-Yorke dimension of the hyperchaotic system is obtained as D_KY = 3.38736, which is a large value. Next, an adaptive control law has been designed to stabilise the novel hyperchaotic system with unknown system parameters. Moreover, an adaptive control law has been designed to achieve global hyperchaos synchronisation of the identical novel hyperchaotic systems with unknown system parameters. MATLAB simulations have been shown in detail to illustrate all the main results developed in this research work.

Keywords: chaos; chaotic systems; hyperchaos; hyperchaotic systems; Lyapunov exponents; adaptive control; adaptive synchronisation; Lyapunov stability theory; exponential nonlinearity; quadratic nonlinearities; simulation.

DOI: 10.1504/IJMIC.2015.070653

International Journal of Modelling, Identification and Control, 2015 Vol.23 No.4, pp.380 - 392

Received: 08 Oct 2014
Accepted: 29 Oct 2014
Published online: 16 Jul 2015 *

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