Research On Multistability Of Fractional-order Memristive Chua's Circuit And Hopfield Neural Network

Memristor,resistor,inductor and capacitor are known as four basic electronic components,among which memristor is widely used in various fields as a nanoscale component with memory characteristics.In recent years,more and more researchers have introduced memristor into nonlinear chaotic circuit system and neural network system,and many complex dynamic phenomena are discovered.It is found that the complex dynamic behavior of the system can be observed by using memristor to replace the electronic components and simulating the synapses of neurons.Compared with integer order system,fractional order system has better characteristics and research value.Based on the fractional order theory,researchers have proposed fractional order chaotic circuit and fractional order neural network system,and achieved some valuable research results.In this thesis,based on the theory of memristor,fractional order theory,traditional Chua circuit and Hopfield neural network,the fractional order memristor Chua circuit system and the fractional order memristor Hopfield neural network system were proposed.Through the study of the internal characteristics of the system,it is found that these two kinds of systems have complex dynamic behavior and multistability phenomenon.The structure of this thesis is as follows.(1)In this thesis,based on the traditional Chua circuit system,an improved fractional delay Chua circuit system is proposed,in which the Chua diode is replaced by a active flux-controlled memristor and a negative conductance in parallel.The system can be regarded as a nonlinear feedback system consisting of a nonlinear element and a linear element with low-pass characteristics.In the complex plane,the nonlinear elements of the system can be expressed approximately by describing the function.Compared with the traditional method,the description function can accurately predict the hidden dynamics,fixed point and unstable behavior of the system.In this paper,the complete mapping of system dynamics in parameter space is given,and the multi stability of the system is analyzed.(2)Considering the memory characteristics of memristor,this paper introduces memristor into Hopfield neural network and proposes a fractional order memristor synaptic coupling Hopfield neural network system based on two neuron.In the system,the memristor is used to simulate the synaptic structure between two neurons.By studying the stability of the linear equilibrium point of the system,the stable region,Hopf bifurcation and folded bifurcation set of the neural network system on the parameter plane are given,and the multistability of the system is analyzed.(3)Considering the mathematical properties of hyperbolic tangent function,the activation function can be simulated by hyperbolic tangent function.This thesis presents a new fractional order hyperbolic memristor Hopfield neural network system based on three neurons.In this system,the synaptic coupling weight of hyperbolic memristor is used to replace the coupling connection weight.By discussing the equilibrium point and dynamic behavior of the Hopfield neural network,the multistability of the system is analyzed.