分数阶Liu混沌系统的Adomian分解法求解及数字实现

Solution to the Fractional-order Liu Chaotic System Based on Adomian Decomposition and its Digital Implementation

针对一类分数阶临界Liu混沌系统,对分数阶微积分采用改进Adomian分解法,从混沌相图、分岔图、复杂度以及分岔空间等方面仿真分析了该分数阶(0.9阶)Liu系统的动力学特性.同时,采用高频率运算数字芯片DSP设计相关程序以及简单硬件电路,实现了分数阶Liu混沌系统.示波器观察结果与仿真结果一致,从数字电路实现方面阐述了系统的混沌特性.

In this research,fractional order Liu chaotic system is studied based on Adomian decomposition method.The dynamic characteristics of the fractional order(0.9 order)Liu system are analyzed from the aspects of chaotic phase diagram,bifurcation diagram,complexity and bifurcation space.At the same time,the fractional Liu chaotic system is realized by using high frequency digital chip DSP and simple hardware circuit.The observation results with oscilloscope are consistent with the simulation results,and the chaotic characteristics of the system are described based on the realization of digital circuit.