Title: Complete amplitude scaling and projective synchronisation of a class of nonlinear dynamical systems
Authors: Vicky Garg; Bharat Bhushan Sharma
Addresses: Electrical Engineering Department, National Institute of Technology, Hamirpur, Himachal Pradesh, 177005, India ' Electrical Engineering Department, National Institute of Technology, Hamirpur, Himachal Pradesh, 177005, India
Abstract: The amplitude control of chaotic systems is important keeping in view different applications of such systems. This paper addresses attaining complete amplitude control by introducing a control function into the nonlinearity of a class of chaotic systems which are having only one nonlinearity. The analytical results presented here show that amplitude of all states of addressed class of chaotic systems can be controlled by introducing control function with the nonlinearity without altering the Lyapunov exponents. Further, the control scheme by applying the Lyapunov stability is presented to realise projective synchronisation of the addressed class of systems by considering the fact that the control function can provide the scale factors. The proposed synchronisation control function is derived using Lyapunov stability theory with typical feature of amplitude scaling without losing chaotic properties. The approach is illustrated using the Genesio system and cubic Chua system as typical examples. The simulation results show the efficacy of proposed approach in achieving amplitude control of all states and the corresponding projective synchronisation under the influence of proposed controller.
Keywords: Lyapunov exponent; amplitude scaling; Genesio system; cubic Chua system; projective synchronisation.
International Journal of Systems, Control and Communications, 2018 Vol.9 No.2, pp.85 - 105
Received: 18 Oct 2016
Accepted: 02 May 2017
Published online: 16 Jan 2018 *