分数阶混沌系统动力学特性分析与DSP实现

Dynamic analysis of the fractional-order chaotic system and its implementation on DSP platform

基于可整合微积分定义,构建了一个新的四维分数阶混沌系统,并利用CADM算法求取分数阶混沌系统数值解。分析了系统参数对分数阶混沌系统动力学特性的影响。用0-1测试验证了该分数阶系统产生混沌的最小阶数。利用SE复杂度算法和C 0复杂度算法获得了该混沌系统随阶数变化的复杂度图。采用数字信号处理器(DSP)完成了该混沌系统的硬件实现。研究结果表明,该系统的分数阶比整数阶拥有更高的复杂度,分数阶混沌系统存在丰富的动力学行为。

Based on the definition of conformable calculus,a new four-dimensional fractional-order chaotic system was constructed,and the numerical solution of the fractional-order chaotic system was obtained using the CADM algorithm.The dynamic characteristics of fractional-order chaotic systems were analyzed by different system parameters.The minimum order of chaos generated by fractional-order systems was verified by the 0-1 test.The complexity graph of the fractional chaotic system that changed with the order was obtained using the SE complexity algorithm and the C 0 complexity algorithm.The digital circuit of the system was implemented on the DSP platform.The results show that the system which is more complex in the fractional order than in the integer order has rich dynamic behaviors.