A novel hyperchaotic system and its complex dynamics

This paper is concerned with a novel four-dimensional continuous autonomous hyperchaotic system, which is obtained by adding a simple dynamical state-feedback controller to a Lorenz-like three-dimensional autonomous chaotic system. This new system contains three parameters and each equation of the system has one quadratic cross-product term. Some basic properties of the system are studied first. Its complex dynamic behaviors are then analyzed by means of Lyapunov exponent (LE) spectrum, bifurcation diagrams, phase portraits and Poincaré sections. It is shown that the system has several large hyperchaotic regions. When the system is evolving in a hyperchaotic region, the two positive LEs are both large, which can be larger than 1 if the system parameters are taken appropriately. The pitchfork bifurcation of the system is finally analyzed by using the center manifold theorem. © 2008 World Scientific Publishing Company.