Bifurcation Analysis And Synchronization Control Of A Kind Of E-HR Neuron Models

The nervous system is made up of billions of neurons,each individually,receiving signals from other cells and generating its own signals to send to its neighbors.When neurons are stimulated,they respond appropriately.When the neuron is in the process of information transmission,by changing the system parameters of the neuron,or under appropriate external conditions,the electric activity of the neuron can show many patterns.Neurons rarely carry out information transmission alone.Collective firing of neurons is the key to information transmission,and synchronization is the manifestation of collective firing.In addition,the synchronization or desynchronization between two or more neurons is a cause of neuronal disease,which can improve the interspike period of neurons,which is closely related to the encoding of information by the brain,therefore,it is of great practical significance to study the firing pattern and synchronization analysis of neurons.Based on a class of e-HR Neuron model,this paper explores the bifurcation law and synchronization control of neurons by combining theoretical knowledge with numerical simulation,which will provide a theoretical basis for neuromedicine.The main contents of this thesis are as follows:The first part is based on the e-HR neuron model.Firstly,the equilibrium points and Hopf bifurcation types of the model are briefly analyzed by using Matcont software.Then,based on the bifurcation diagram of single parameter and double parameter,time response diagram and phase trajectory diagram,the bifurcation behavior of the system on the plane of single parameter and double parameter is discussed.In the second part,the flux e-HR neuron model is established on the basis of e-HR Neuron model considering the influence of external electromagnetic induction.Firstly,the discharge pattern of the flux e-HR neuron model is explored by combining theoretical knowledge with numerical simulation under different external stimuli,and the hidden discharge behavior of the model is controlled by Washout controller,from an unstable state to a stable state.Then,the bifurcation structure of the magnetic flux e-HR neuron model on the single-parameter and two-parameter plane is simulated by Matlab software.In the third part,based on e-HR model and flux e-HR model respectively,the synchronization of e-HR model coupled by memristors and e-HR model coupled by electric coupling is studied by using nonlinear adaptive synchronization method.Considering the unpredictability of the parameters in the neuron model,parameter identification is introduced to realize the synchronization control.