Complex State Variables Based Novel Hyperchaotic System with Nine Equilibria

Abstract

This paper posit a novel three dimensional autonomous chaotic system. A six dimensional system is derived from the proposed three dimensional autonomous chaotic system by considering its real state variables as complex state variables. The derived system has nine equilibria and shows hyperchaotic 3-torus behaviour. Basic dynamical properties like types of equilibrium point, symmetry, invariance, dissipation, Lyapunov exponent, Lyapunov dimension are calculated and analysed for both the real and complex valued systems. Different qualitative and quantitative tools such as time series, phase plane, Lyapunov exponent spectrum and Lyapunov dimension are used to analyse different dynamic behaviours of both real and complex valued system. MATLAB simulation environment is used for the effective verification of the numerical or theoretical approach. Simulation results reveal that objectives are achieved successfully.