关键词: 一个非线性项, 混沌, 四维超混沌系统, 线性反馈同步控制, 自适应同步控制

Abstract: In order to study the nature of chaos, a four-dimensional hyperchaos system with only one nonlinear term was constructed. In this paper the complex dynamics features including hyperchaos attractor, the Lyapunov exponent and the Poincare map were studied which proved the hyperchaos system's chaotic behavior. In order to better control this four-dimensional hyperchaotic system, the control simulation of the system was given respectively by the linear feedback control and adaptive control method which shows that linear feedback control method and the adaptive control method are effective and feasible to control the hyperchaos system with only one nonlinear term. At the same time, the advantages and disadvantages of the two kinds of control methods in controlling chaos system were compared.

Key words: Single nonlinear term, chaos, Four-dimensional hyperchaos system, linear feedback synchronization control, adaptive synchronization control