Dynamic Analysis And Network Spiking Synchronization Of The AEIF Neuron Model

In this thesis,the adaptive exponential integration-and-fire model(aEIF)is used to study the control effect of different parameters on the response pattern of neurons,and further discuss the effect of network structure and initial membrane potentials on network synchronization.This thesis first analyzes the dynamics of the aEIF neuron model,and finds that the input current I can influence the number of fixed points of the neuron system,and then influence the stable resting state or excited state of the neuron.During the transition from the resting state to the excited state,the system experiences saddle-node bifurcation or Hopf bifurcation depending on the parameters.Then the effects of input current,membrane potentials reset parameters and adaptive current reset parameters on the response pattern of aEIF neurons are analyzed by using phase diagram,nullcline and bifurcation diagram.Finally,the effect of network structure and initial membrane potentials on network synchronization is discussed in neuronal networks.There are two main innovations in this thesis:first,a synchronization index describing the synchronization state of the network and a response time difference describing the impact degree of the neurons in the coupled network are proposed for the periodic firing response;second,the initial membrane potential of the neuronal network has an influence on the synchronization effect when the network reaches phase lock,which is verified by numerical simulation.It is found that some neurons in the neuronal network play a dominant role in the transmission of stimulus signals,and they are defined as primary neurons.With the help of primary neurons and network topology,the neurons in the network can be graded and the signal transmission order map can be obtained,which will become a powerful tool to study the fire order of neurons in the network in the phase locked state.In addition,when the network size is the same and the initial membrane potential and the number of connected edges are the same,the increase of the number of connected edges of primary neurons can promote the synchronization effect of the network.