Eur. Phys. J. Special Topics 228, 2197-2214 (2019)
https://doi.org/10.1140/epjst/e2019-900036-5

Regular Article

Memristor-based novel complex-valued chaotic system and its projective synchronisation using nonlinear active control technique

¹ Department of Electrical Engineering, National Institute of Technology Meghalaya, Shillong, Meghalaya 793003, India
² Department of Electrical Engineering, National Institute of Technology Silchar, Silchar, Assam 788010, India

^a e-mail: piyushpratapsingh@gmail.com

Received: 15 February 2019
Received in final form: 20 May 2019
Published online: 14 October 2019

Abstract

In this paper, a flux controlled memristor-based novel complex-valued chaotic system and its projective synchronisation is investigated. The proposed complex-valued chaotic system has line and plane of equilibria, i.e. an infinite number of equilibria. Different qualitative and quantitative tools such as time series, phase plane, Poincaré section, Lyapunov exponents, Lyapunov spectrum, and Lyapunov dimension are used to evidence the chaotic behaviour of the proposed complex-valued system. Further, the projective synchronisation between the proposed complex-valued chaotic systems is achieved using nonlinear active control. Active control laws are designed, by using sum of the relevant variables of the proposed complex-valued chaotic systems, to ensure the convergence of error dynamics. The required global asymptotic stability condition is derived using Lyapunov stability theory. Simulation is done in MATLAB environment to verify the theoretical approach. Simulation results reveal that the objectives of the paper are achieved successfully.