非线性系统的隐藏吸引子及组合同步

Hidden Attractors and Combine Synchronization of Nonlinear System

研究了一个四维分数阶新系统的隐藏吸引子.在特定条件下,此系统有一条平衡点线或无平衡点.同时讨论了系统平衡点的稳定性,证明了不同类型的隐藏吸引子.进一步通过调整系统参数和系统初始值,利用分岔图、相图得到了新系统的共存隐藏吸引子,分析了系统的复杂动力学行为,并设计了同步控制器,实现了此系统的组合同步,数值仿真结果验证了同步控制方案的有效性.

This paper presents a novel 4D fractional order chaotic system with interesting dynamics characteristics.Especially, the system has a line of equilibrium points or no equilibrium points under certain conditions.Compared with other fractional order systems, the new system has richer dynamic properties.Furthermore, various hidden attractors can be obtained from this fractional order system.In addition, the coexisting hidden attractors are observed by adjusting initial values and system parameters.The complex hidden dynamics behaviors are demonstrated by phase portraits, bifurcation diagrams numerically.Besides, the combination synchronization of the new fractional order system is realized by numerical simulations.