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.