一类简单二次非线性 Sprott混沌系统的分析与控制

摘要

The control problems of a class of nonlinear Sprott simple chaotic systems were solved via an adaptive backstepping method.Firstly,the conditions of stability of the equilibria point and the existence of Hopf bifurcation were obtained.Secondly, chaotic phenomenon of the system was verified by means of presenting Lyapunov exponent and chaotic attractor,and complex dynamic behaviors were found via analyzing bifurcation diagram.Finally,an adaptive backstepping controller was designed to control chaotic system to a given equilibrium point.Numerical simulation has shown the effectiveness of the controller designed.%用自适应反推方法考虑一类简单非线性 Sprott 混沌系统的控制问题，得到了平衡点的稳定性及 Hopf 分岔存在性的条件，通过 Lyapunov 指数图及混沌吸引子验证了系统的混沌现象，通过分岔图分析得到了系统存在复杂动力学行为，并设计自适应反推控制器控制混沌系统到给定的平衡点。数值仿真验证了所设计控制器的有效性。