Eur. Phys. J. Special Topics 229, 1265-1278 (2020)
https://doi.org/10.1140/epjst/e2020-900259-0

Regular Article

A novel chaotic system without equilibria, with parachute and thumb shapes of Poincare map and its projective synchronisation

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

^a e-mail: piyushpratapsingh@gmail.com

Received: 1 November 2019
Received in final form: 30 December 2019
Published online: 26 March 2020

Abstract

In this paper, a three-dimensional novel chaotic system and its projective synchronisation are investigated. The proposed chaotic system has no equilibria. The topological structure of proposed chaotic system is different form Lorenz, Rossler and Chen systems. Different qualitative and quantitative tools such as time series, phase plane, Poincare section, bifurcation plot, Lyapunov exponents, Lyapunov spectrum, and Lyapunov dimension are used to evidence the chaotic behaviour of the proposed system. Further, the projective synchronisation between the proposed chaotic systems is achieved using nonlinear active control. Active control laws are designed, by using sum of the relevant variables of the proposed 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.