一种分数阶混沌系统的通用增强型FPGA实现  

A universal enhanced FPGA implementation of the fractional-order chaotic system

作　　者：彭代鑫 彭良玉 张学丰 PENG Dai-xin;PENG Liang-yu;ZHANG Xue-feng(School of Physics and Electronic,Hunan Normal University,Changsha 410081,China)

机构地区：[1]湖南师范大学物理与电子科学学院,长沙410081

出　　处：《信息技术》2024年第1期115-121,共7页Information Technology

摘　　要：针对目前分数阶混沌系统的FPGA设计实现通用程度不高的问题,文中给出了一种通用增强型FPGA算法。首先给出基于G-L定义的分数阶微分算法原理,再将一个已知的三维整数阶混沌系统扩展至分数阶多涡卷混沌系统,通过平衡点、分岔图及最大李氏指数谱分析了其动力学特性,最后运用可变长度移位寄存器,设计分数阶微分的通用增强型FPGA算法,并将其应用至分数阶多涡卷混沌系统。实验结果与数值仿真结果一致,该算法当修改参数时,无需设计新的代码,并能够动态调节记忆长度,且对步长没有严格限制。In order to solve the problem of the low degree of general purpose of the FPGA design and implementation of fractional-order chaotic system,a universal enhanced FPGA algorithm is presented in this paper.Firstly,the principle of fractional differential algorithm based on G-L definition is given.Then,a known three-dimensional integer-order chaotic system is extended to fractional multi-scroll chaotic system,and its dynamic characteristics are analyzed by means of equilibrium points,bifurcation diagrams and maximum Lyapunov exponential spectrum.Finally,a universal enhanced FPGA algorithm of fractional-order differential is designed by using variable length shifting registers,and it is applied to the fractional-order multi-scroll chaotic system.Experiment results are consistent with the results of numerical simulations,when modifying parameters in this algorithm,there is no need to design a new code,and the memory length can be dynamically adjusted,and there is no strict limit on step.

关 键 词：分数阶 多涡卷 混沌系统 FPGA 

分 类 号：TP271[自动化与计算机技术—检测技术与自动化装置]