不同维异结构分数阶忆阻混沌系统的同步电路仿真

Synchronization Circuit Simulation of Fractional Memristor Chaotic Systems with Different Dimensions and Different Structures

将一类整数阶忆阻混沌系统推广到分数阶,首先对其进行数值仿真并在Multisim软件中对其进行电路设计,电路仿真与数值仿真结果一致。然后根据主动控制原理及分数阶系统稳定性理论,以分数阶忆阻混沌系统与分数阶Liu系统为控制对象,设计控制器,利用升维的方法研究了两个不同维系统的异结构同步,并在Multisim软件中完成了同步电路的设计与仿真,仿真结果表明了控制器的有效性。该文研究的分数阶忆阻混沌系统及其同步电路的设计能够结合仿真软件进行教学,使抽象的理论教学变得生动具体,为非线性系统理论、非线性电路设计等课程的教学提供新的思路与方法。

A class of integer order memristor chaotic system is extended to fractional order.Firstly,numerical simulations are carried out,then circuit of the system is designed in Multisim software,and the circuit simulation results are consistent with the numerical simulation results.Next,according to the active control principle and the stability theory of fractional order systems,taking the fractional order memristor chaotic system and fractional Liu system as the control objects,the controllers are designed,and the synchronization of the two systems with different dimensions and different structures are studied by the methods of dimension increase.Finally,the two synchronization circuits are realized in Multisim software,and the simulation results show the effectiveness of the controller.The design and implementation of fractional memristor chaotic system and its synchronization circuits studied in this paper can be combined with simulation software for teaching,which makes the abstract theory teaching vivid and concrete,and provides new ideas and methods for the teaching of nonlinear system theory,nonlinear circuit design and other courses.