Research On Chaotic Dynamics Of Locally Active Memristor

Memristors are nonlinear resistors with memory,which have significant potential applications in new memories,digital logic circuits,artificial neural networks,and oscillating circuits because of its nanoscale,adjustable resistance and non-volatility.In 2014,Chua defined the locally active memristor,which has negative resistance on the DC V-I plot,so the memristors can be classified as passive memristors and locally active memristors.Passive memristor with bionic functions is often used to simulate biological synapses.Locally active memristors can amplify weak signals and simulate the neuromorphic behavior of neurons.The memristor-based neuromorphic network has the ability to break the Von Neumann architecture of the separation of storage and calculation,which has become one of the best candidates for building a new generation of computers and neural networks.However,the neural network with computing in-memory is in the preliminary research stage.Many fundamental theories need to be further studied and explored,such as modeling and characteristics of locally active memristor,oscillation mechanism of memristor-based oscillator,and neuromorphics of memristor-based neurons.This thesis studies the essential characteristics of locally active memristors and their applications in oscillation circuits and neuromorphic dynamics.A novel three-valued locally active memristor model is designed,and then the memristor-based oscillation circuit and the memristor-based neuron are constructed,whose complex dynamics and oscillation mechanism are studied.The main innovative work of this thesis is as follows:(1)Based on Chua’s unfolding theorem,a new three-valued generic locally active memristor model is designed.The basic characteristics of the memristor,including non-volatility and local activity,are analyzed by using the v-i pinched hysteresis loops,power-off plot,and DC V-I plot of the memristor.Theoretical and simulation analysis shows that the memristor is globally passive but locally active.It has two different locally active domains(the locally active domain with stable operating points and the locally active domain with unstable operating points)and three stable equilibrium points,so it also has non-volatility of resistance(or conductance).(2)A small-signal equivalent circuit is established for the two locally active domains of the memristor using the small-signal analysis method.According to the frequency response of the small-signal equivalent admittance function,the oscillation conditions,oscillation frequency and oscillation circuit of the memristor operating in its locally active domains are theoretically obtained.Through the poles and frequency response of the admittance function of the memristor circuit,the edge of chaos domains of the second-order and third-order circuits are obtained.The edge of chaos is astable locally active domain.However,under the disturbance of circuit parameters,the eigenvalues of the circuit equation and the poles of the admittance function can be moved from the edge of chaos domain to the unstable locally active domain,thereby causing the periodic and chaotic oscillations through the Hopf bifurcation theorem.The Hopf bifurcation and oscillation mechanism of the locally active memristor-based circuit are revealed.From the perspective of the locally active memristor,it is proved that the complex periodic and chaotic oscillations originate from the locally active domain near the edge of chaos of the memristive circuit.(3)In order to further explore the complex characteristics of locally active memristors,second-order and third-order neuron models are constructed based on the designed locally active memristor model.A variety of neuromorphic behaviors are produced under the condition of appropriate input voltage and circuit parameters,such as single spiking and periodic spiking,self-sustained oscillation,chaotic oscillation,Burst-number adaptation,refractory period behavior,spike latency behavior,all-or-nothing discharge behavior,tonic spiking behavior,and phasic spiking behavior.The machenism of neuromorphic dynamics of two neuron models are analyzed by theory and simulation,and it is proved that the abundant neuromorphic behaviors of neurons mostly occur on or near the edge of chaos.