基于Adomian分解法的分数阶忆阻混沌电路分析及其FPGA实现  

Analysis and FPGA implementation of fractional-order memristive chaotic circuit based on Adomian decomposition

作　　者：张哲源 吴朝俊 张琦 杨宁宁[3] ZHANG Zheyuan;WU Chaojun;ZHANG Qi;YANG Ningning(School of Electronics and Information,Xian Polytechnic University,Xian710048,China;Xian Key Laboratory of Interconnected Sensing and Intelligent Diagnosis for Electrical Equipment,Xian710048,China;School of Electrical Engineering,Xian University of Technology,Xian710048,China)

机构地区：[1]西安工程大学电子信息学院,陕西西安710048 [2]西安市电气设备互联感知与智能诊断重点实验室,陕西西安710048 [3]西安理工大学电气工程学院,陕西西安710048

出　　处：《电子元件与材料》2023年第11期1340-1347,共8页Electronic Components And Materials

基　　金：国家自然科学基金(51507134);陕西省自然科学基础研究计划面上项目(2021JM-449,2018JM5068)。

摘　　要：基于忆阻器的分数阶混沌系统相较于整数阶能更加准确地描述系统的动力学行为。首先采用一个三次光滑非线性忆阻器构建了基于忆阻器的混沌系统,通过李雅普诺夫指数、分岔图等方法分析了系统的动力学行为。其次将该系统推广到分数阶,获得了阶次q为0.9时,不同参数下的系统相图。通过分岔图对系统进行动力学行为分析,与相图对比发现所描述状态一致。最后基于Adomian分解法实现了该分数阶系统的FPGA硬件电路实验。实验结果与数值仿真结果一致,从而进一步验证了该忆阻混沌系统理论分析的正确性与可行性,为其在加密领域的应用积累了理论基础。Compared with integer-order systems,fractional-order chaotic systems,based on memristors,is more accurate to describe the dynamic behavior of a system.Firstly,a chaotic system was constructed using a cubic smooth nonlinear memristor,and the dynamic behavior of the system was analyzed through Lyapunov exponents,bifurcation diagrams,and other methods.Secondly,the system was extended to the fractional-order domain,and phase diagrams of different parameters of the system were obtained at the order q=0.9.By comparing the dynamical behavior of the system determined by bifurcation diagram and the fractional-order domain phase diagram,it is found that the results are consistent.Finally,the Adomian decomposition method was used to implement the fractional-order system in FPGA hardware circuit.The experimental results are consistent with the numerical simulation results,which further verifies the correctness and feasibility of the theoretical analysis of the memristive chaotic system,and enriches the theoretical foundation for its application in the field of encryption.

关 键 词：分数阶 忆阻混沌系统 ADOMIAN分解法 动力学特性 FPGA实现 

分 类 号：O415.5[理学—理论物理] TN60[理学—物理]