Title: A novel 4-D hyperchaotic system with two quadratic nonlinearities and its adaptive synchronisation

Authors: Sundarapandian Vaidyanathan; Ahmad Taher Azar; Abdesselem Boulkroune

Addresses: Research and Development Centre, Vel Tech University, Avadi, Chennai,600062, Tamil Nadu, India ' Faculty of Computers and Information, Benha University, Egypt; Nanoelectronics Integrated Systems Center (NISC), Nile University, Egypt ' LAJ Laboratory, University of Jijel, BP. 98, Ouled-Aissa, 18000 Jijel, Algeria

Abstract: This work announces an eleven-term novel 4-D hyperchaotic system with two quadratic nonlinearities. A qualitative analysis of the properties of the novel 4-D hyperchaotic system is presented. A special feature of our novel hyperchaotic system is that it has three equilibrium points of which two are unstable and one is locally asymptotically stable. The Lyapunov exponents of the novel hyperchaotic system are obtained as L₁ = 1.5146, L₂ = 0.2527, L₃ = 0 and L₄ = -12.7626. The Kaplan-Yorke dimension of the novel hyperchaotic system is derived as D_KY. = 3.1385. Next, this work describes the design of an adaptive controller for the global hyperchaos synchronisation of identical novel hyperchaotic systems with unknown parameters. MATLAB simulations are shown to describe all the main results derived in this work.

Keywords: chaos; hyperchaos; chaos control; chaos synchronisation; adaptive control.

DOI: 10.1504/IJAAC.2018.088612

International Journal of Automation and Control, 2018 Vol.12 No.1, pp.5 - 26

Received: 15 Oct 2016
Accepted: 28 Nov 2016
Published online: 13 Dec 2017 *

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