Boundary Dynamics Analysis And Synchronization Control Of Memristive Neuron Systems

In a neural network,the connection and information transmission between brain neurons are completed by synapses.Synapses also provide the brain with highly parallel processing capabilities and are an indispensable part of the neural network.The memristor is a kind of non-linear resistance with memory characteristics.Its transmission characteristics are very similar to neuronal synapses.A single memristor can simulate the basic functions of a synapse to reduce system energy consumption and reduce the complexity of integrated circuits.The effect of degrees.Therefore,memristors are often used to simulate synapses in neuronal systems to form new neuronal systems.In this theisis,two groups of memristive neuron systems are discussed.Based on the flow switching theory,the necessary and sufficient conditions for the crossing motion,edge rubbing motion and synovial motion of the system are derived at the separation boundary.The boundary dynamics of the system is analyzed and the coupling is realized.Synchronous control of neurons completes the hardware circuits of the two systems.The main research contents of this paper are as follows:(1)For the FitzHugh-Nagumo memristive neuron system,use the magnetic flux-charge analysis method to study the dynamic behavior of the neuron boundary in the Weiku domain,and explore the dynamic characteristics of the system such as coexistence and bifurcation and extreme multi-stability.Based on the flow switching theory,the G-function of the system is given,and the conditions that the G-function meets when the switching motion is performed at the boundary are analyzed.The bifurcation diagram,Lyapunov exponent,two-parameter distribution diagram,and attraction basin are used to explore different memories.Under the conditions of initial resistance,system parameters,and initial values,the system has multiple switching motions at the boundary,such as crossing motion and edge rubbing motion,presenting a different switching mapping structure,analyzing the extreme multi-stability and coexistence of the system,etc.Promote the understanding of the switching mechanism.Finally,a detailed dynamic analysis of the switching motion at the boundary is carried out,and the correctness of the analytical conditions of the flow switching theory is verified.(2)For the Hindmarsh-Rose memristive neuron model,based on the flow switching theory,this discontinuous dynamic system is analyzed on its coexistence bifurcation,discharge phenomenon and boundary dynamic characteristics.Analyze the G function of the HR system and the necessary and sufficient conditions for the occurrence of the switching movement through the flow switching theory.Through bifurcation diagrams,phase diagrams,and dual parameter diagrams,the boundary bifurcation and coexistence phenomena under different mapping structures of the system are discussed.The various discharge activities in the HR system are observed from the phase diagrams and timing diagrams,and different external stimuli are analyzed.The effect of electric current on the electrical activity of neurons.In addition,the distribution of the G function in different regions when the system performs boundary switching motion is analyzed from the mapping trajectory diagram,and the feasibility of the theory is proved by numerical simulation.(3)The digital circuit experiment of the two memristive neuron system is realized,and the feedback control method is designed to implement the coupled neuron for synchronous control.First,use Verilog language and FPGA development board to build the digital module circuit of the system,observe the different state attractor trajectory diagrams and timing diagrams of FHN neurons and HR neurons from an oscilloscope to verify the accuracy of the numerical simulation.In addition,two homogenous neurons are coupled through synapses to study the synchronization control of coupled neurons.Couple two identical FHN neurons through electrical synapses,discuss the influence of electrical coupling coefficients on the synchronization of coupled neurons;then,consider the coupled HR neuron model under the electromagnetic induction effect,design an adaptive controller and unknown parameter identification,Realize the synchronous control of the coupled system.