A new 4D hyperchaotic system and its control

Abstract

This paper presents a new four-dimensional (4D) hyperchaotic system by introducing a linear controller to 3D chaotic Qi system. Based on theoretical analysis and numerical simulations, the dynamical behaviors of the new system are studied including dissipativity and invariance, equilibria and their stability, quasi-periodic orbits, chaotic and hyperchaotic attractors. In addition, the Hopf bifurcation at the zero equilibrium point and hyperchaos control of the system are investigated. The numerical simulations, including phase diagram, Lyapunov exponent spectrum, bifurcations and Poincaré maps are carried out in order to analyze and verify the complex phenomena of the 4D hyperchaotic system.