A hyper-chaos with only one nonlinear term and its adaptive synchronization and control

Chaos is widespread in natural session, which is one of typical nonlinear system. This paper gave a four-dimensional nonlinear dynamic system with only one nonlinear term. And it also analyzed its complex dynamic characteristics, including the space trajectory, the Lyapunov exponent, the Poincare map, the Time-domain waveform diagram and the Bifurcation map. These characteristics indicate that the four-dimensional dynamical systems contain hyper-chaotic attractors. It designed adaptive controller, and achieved the system´s synchronization and control. The results show that using adaptive synchronization and control methods can be an ideal way to eliminate the chaos, so that the hyper-chaotic system can reach a stable state, and also show the validities and feasibilities of adaptive synchronization and control methods to control hyper-chaotic dynamical systems.