Analysis of a New Hyperchaotic System Based on a Chaotic System

摘要

This paper reports a new four-dimensional continuous autonomous hyperchaotic system obtained by adding a state feedback controller to a three-dimensional autonomous chaotic system. The new system has two parameters, and each equation of the system has one quadratic cross product term. Some basic properties of this system are analyzed. The complex dynamic behaviors of the system are studied by the Lyapunov exponent spectrum and bifurcation diagrams. The system has several larger hyperchaotic regions. When the system is hyperchaotic, the two positive Lyapunov exponents are both large and they are both larger than 1 if the system parameters are taken appropriately.