A new four-dimensional chaotic attractor

Abstract

A new four-dimensional chaotic system is introduced in this paper, it is mainly consist of four multiplier terms and four simple terms. The system has different structure and topology of existing four-dimensional systems and produces two equilibrium points with one at the origin. The fundamental characteristics of the new system are investigated by means of equilibrium points, their stabilities, power spectrum, bifurcation diagram, and Poincaré map. Furthermore, an optimal controller using Riccati equation is established to run system trajectories to the zero equilibrium. The dynamics of the new system is simulated using Matlab and Simulink. Keywords: Chaos attractor, Lyapunov exponents, Bifurcation diagram, Poincaré map, Riccati equation, Stability