具有唯一平衡点的四维超混沌Lü-like系统的研究

Study on a4D Hyperchaotic Lü-like System Only with One Equilibrium

基于三维Lü混沌系统,利用反馈控制技术,提出了一个具有5个参数和3个非线性项的新四维自治超混沌系统,并研究该系统的动力学性质;所得新系统具有唯一平衡点,讨论了对应平衡点的稳定性,同时严格证明了Hopf分岔的局部动力学行为;进一步通过分岔图、Lyapunov指数及Poincaré映射等数值分析,验证了系统的超混沌吸引子、混沌吸引子及周期吸引子的存在性。

Based on three-dimensional （3D） Lti chaotic system, and with the help of feedback control techniques, this paper reports a new 4D autonomous hyperchaotic system with five parameters and three nonlinear items, analyzes the dynamic properties of the system, as the new system has only one equilibrium, and studies the stability of corresponding equilibrium. Meanwhile the local dynamics such as Hopf bifurcation is rigorous derived; in addition, numerical analysis of phase trajectories, bifurcation and Lyapunov exponents verifies the existence of the hyperchaotic attractor, chaotic attractor and periodic attractor.