Title: Design and SPICE implementation of a 12-term novel hyperchaotic system and its synchronisation via active control

Authors: Sundarapandian Vaidyanathan; Ahmad Taher Azar; Karthikeyan Rajagopal; Prasina Alexander

Addresses: Research and Development Centre, Vel Tech University, Avadi, Chennai-600 062, Tamil Nadu, India ' Faculty of Computers and Information, Benha University, Egypt ' Department of Electronics and Communications Engineering, Chennai Institute of Technology, Kundrathur, Chennai-600 069, Tamil Nadu, India ' Department of Electronics and Communications Engineering, Chennai Institute of Technology, Kundrathur, Chennai-600 069, Tamil Nadu, India

Abstract: This research work describes the design and SPICE implementation of a 12-term novel hyperchaotic system with four quadratic nonlinearities. The Lyapunov exponents of the dissipative novel hyperchaotic system are obtained as L₁ = 4.1043, L₂ = 0.1571, L₃ = 0 and L₄ = −34.2529. The maximal Lyapunov exponent (MLE) of the novel hyperchaotic system is L₁ = 4.1043. The Lyapunov dimension of the hyperchaotic system has been obtained as D_L = 3.1244. The qualitative properties of the novel hyperchaotic system are described in detail. Moreover, the hyperchaotic system has been implemented in LTspice IV (SPICE simulator) and the outputs are obtained in SPICE showing hyperchaos of the novel system. Next, active control method has been applied for the global synchronisation of the novel hyperchaotic systems and the synchronisation result has been proved using Lyapunov stability theory. The active controller for the global synchronisation of the identical novel hyperchaotic systems has been implemented in LTspice IV and the SPICE simulation results have been detailed.

Keywords: chaos; chaotic systems; hyperchaos; hyperchaotic systems; Lyapunov exponents; SPICE implementation; synchronisation; active control; quadratic nonlinearities; nonlinear systems; stability theory; simulation.

DOI: 10.1504/IJMIC.2015.069936

International Journal of Modelling, Identification and Control, 2015 Vol.23 No.3, pp.267 - 277

Received: 03 Mar 2014
Accepted: 01 Aug 2014
Published online: 16 Jun 2015 *

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