The generation of a hyperchaotic system based on a three-dimensional autonomous chaotic system

This paper reports a new four-dimensional hyperchaotic system obtained by adding a 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 the new system are analysed. The different dynamic behaviours of the new system are studied when the system parameter a or b is varied. The system is hyperchaotic in several different regions of the parameter b . Especially, the two positive Lyapunov exponents are both larger and the hyperchaotic region is also larger when this system is hyperchaotic in the case of varying a . The hyperchaotic system is analysed by Lyapunov-exponents spectrum, bifurcation diagrams and Poincaré sections.