具有无穷平衡点的新混沌系统动力学分析与振动控制

摘要

提出了一个新的三维混沌系统,对它奇特的动力学行为展开了理论分析和数值仿真.此系统具有无穷多个平衡点,全部位于一个平面的双曲线上.在状态和参数的组合变换下,系统能生成对称的隐藏吸引子.在双参数的对称变换下,混沌具有不变性.同时,系统轨道出现了大幅度的跃迁现象.最后,设计出单参数调节的线性状态反馈控制器,在有限时间内消除混沌.%A novel three-dimensional chaotic system was presented.Its strange dynamical behaviors were investigated by theoretical analysis and numerical simulations.The system has infinite equilibria locating on a hyperbola in a plane.Symmetric hidden attractors can be generated via a combinational transformation on states and parameters.The chaos is invariant under a double-parameter symmetric transformation.Simultaneously,a larger orbital transition phenomenon appears.Finally,a linear state feedback controller with an adjustable parameter was designed to eliminate the chaos within a finite time.