基于Adomian分解算法的新型分数阶混沌系统特性分析与FPGA实现

Characteristic analysis and FPGA implementation of a novelfractional-order chaotic systemby Adomian decomposition algorithm

混沌电路实现是混沌研究的基础,目前混沌系统的FPGA实现多数采用在MATLAB DSP Builder平台搭建模型实现,由于分数阶积分器难于构造,该方法适合实现整数阶混沌系统,同时其他基于分数阶微积分算法的编程实现方法原理复杂,消耗资源多。针对上述问题,提出了一个新型混沌系统,通过Lyapunov指数,分岔图,平衡点等手段对系统的动力学行为进行了数值分析,进一步将其拓展到分数阶,给出了系统阶次q为0.8时不同状态下的相图,其结果与分岔图所描述的状态吻合。最后,采用Adomian分解法实现了该分数阶系统的FPGA硬件电路,通过示波器观察到混沌相图与数值仿真结果一致,从而验证了该分数阶混沌系统理论分析的正确性及可行性。

The realization of chaotic circuits is the basis of chaotic research,and at present most FPGA implementations of chaotic systems are implemented by using the MATLAB DSP Builder platform to build models.Because fractional integrators are difficult to construct,this method is suitable for realizing integer-order chaotic systems.At the same time,other programming methods based on fractional calculus algorithms have complex principles and consume more resources.In response to the above problems,a new type of chaotic system is proposed,with the dynamic behavior of the system numerically analyzed by means of Lyapunov exponents,bifurcation diagrams,equilibrium points,etc.It is further extended to the fractional order,giving the system order q of 0.8,with the results of the phase diagrams under different states being consistent with the states described in the bifurcation diagram.Finally,the FPGA hardware circuit of the fractional-order system is realized by the Adomian decomposition method.The chaotic phase diagrams are consistent with the numerical simulation results observed through the oscilloscope.This verifies the correctness and feasibility of the theoretical analysis of the fractional chaotic system.