基于分数阶忆阻器的混沌电路动力学行为分析与同步研究

项目名称： 基于分数阶忆阻器的混沌电路动力学行为分析与同步研究

项目编号： No.51507134

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 电工技术

项目作者： 杨宁宁

作者单位： 西安理工大学

项目金额： 20万元

中文摘要： 忆阻器的记忆特性与分数阶微积分的记忆、遗传特性有着本质上相同的数学原理。根据实际忆阻器的电学特性构建其分数阶模型对分析和研究基于忆阻器的各类系统具有重要意义和实用价值。本课题首先拓展整数阶忆阻器数学模型为分数阶形式，并搭建通用分数阶忆阻器电路模拟器，在此基础上揭示单个分数阶忆阻器及多个分数阶忆阻器互联的记忆特性规律。其次，提出一种基于分数阶忆阻器的混沌电路设计方法，并采用该方法构造分数阶忆阻器蔡电路，以明确此类分数阶忆阻器混沌电路系统的复杂动力学行为与忆阻器阶次参数的关系，并对求取此类系统最小阶次的方法进行研究。最后，采用分数阶忆阻器实现细胞神经网络单元，对基于分数阶忆阻器细胞神经网络混沌电路的构造方法进行研究，以解决结构不同或参数不确定情况下分数阶忆阻器混沌电路有限时间广义同步问题。研究结果不仅对忆阻器的实现具有重要的工程应用价值，同时对忆阻器在神经网络等领域的应用具有重要的学术意义。

中文关键词： 分数阶微积分；分数阶忆阻器；分数阶混沌电路；细胞神经网络；有限时间同步控制

英文摘要： Memory properties of memristors and memory, hereditary properties of fractional calculus have essentially the same mathematical principle. The establishment of fractional-order memristor's model according the electrical characteristics of actual memristors has important significance and application value for the analysis and research of all kinds memristor-based systems. In this project, firstly，the mathematical model of the integer-order memristor is expanded to the fractional-order form and the general fractional-order memristor simulator circuit is built. The law of memory characteristics of single fractional-order memristor and plurality of fractional-order memristors interconnection are revealed. Secondly, a new systematic design approach for the fractional-order memristor-based chaoitc circuits is inroduced. By this method，a class of fractional-order memristor-based Chua's circuits is constructed. The relationship between the complex dynamical behaviors of this kind of chaotic circuits and the order parameters of memristor is made clear. Then，A study on calculating the minimum order of this kind of system is conducted. Finally, Cellular Neural Network(CNN) unit is implemented with the fractional-order memristor. Researches on the method of designing CNN-based fractional-order memristive chaotic circuit are carried on to solve the problem of finite-time synchronization control of fractional-order memristor-based chaoitc circuits with different structure or unknown parameters. Results of the research not only have important engineering application value for the realization of the memristor, also have important academic significance to the application of the memristor in the fields of neural network.

英文关键词： Fractional Calculus;Fractional-Order Memristor;Fractional-Order Chaotic Circuit;Cellular Neural Networks;Finite-time Synchronization Control