一个新三维分数阶动力系统

通过微分方程结构的变化给出了一个不同于以往的三维自治混沌系统和对应的新分数阶动力系统,其吸引子相图的拓扑结构与以往系统不同。首先给出了新构造整数阶动力系统的吸引子相图和Lyapunov维数等基本动力学特性;然后基于分数阶稳定性理论和数值计算对分数阶混沌系统平衡点进行了分析,得出在阶数qi0.738,i=1,2,3时系统是稳定的,并进而给出了Caputo意义下阶数为q=0.92、q=0.93时的吸引子相图;最后讨论了在q=0.95时固定其他系统参数时,系统的动力学行为随参数a的变化。

A New Three Dimensional Fractional Order Dynamical System

Based on the change of differential equation structure to give out a three dimensional autono-mous chaotic system which is different from past and corresponding new fractional order dynamical system and the topological structure of its attractor phase diagram is different from previous systems.First,give the attractor phase diagram and basic dynamic characteristics such as Lyapunov dimensionality of newly es-tablished integer order dynamical system;then based on the fractional order stability theory and numerical calculation to analyze the balance point of fractional order chaotic system,obtain that the system is stable when the order qi<0.738,i=1,2,3,then give out the attractor phase diagram when the order is q=0.92, q=0.93 in the sense of Caputo;finally discuss the change of system dynamic behavior along with parameter when the other system parameters are fixed under the condition of q=0.95.