A New 4D Four-Wing Hyperchaotic Smooth Autonomous System and Its Improved Form

This paper presents a novel four-dimensional (4D) smooth autonomous system. The prosposed system is special since it has only one equilibrium, but it can generate a four-wing chaotic or hyperchaotic attractor. By applying either analytical or numerical methods, some basic properties of the 4D system, such as phase diagrams, bifurcation diagram and Lyapunov exponents are investigated to observe chaotic motions. And the improved form is proposed by introducing changeable sine periodic signal into one of the state variable of the 4D system. It is confirmed that the improved 4D system always holds two invariable positive Lyapunov exponents when the external sine periodic signal works, and still displays four-wing hyperchaotic behaviour.