Dynamical Analysis And Firing Properties Of Neurons

Neuron is the basic unit of the nervous system.The firing properties of neurons determine the function of the neural network.Various neuron models have different nonlinear characteristics,so that the neurons have different firing properties.This thesis studies the firing properties and influence of model parameters on firing properties of different neurons,fits the parameters of neuron models according to their firing properties,and explores the effects of neuron properties on neural network coding.Firstly,the dynamic characteristics of two-dimensional and three-dimensional Prescott models under external electrical stimuli are studied by analytic method.The effects of important electrophysiological parameters and adaptive currents on equilibrium distribution,saddle-node bifurcation,Hopf bifurcation and critical bifurcation points are discussed.The analytical expressions of the type of Hopf bifurcation are derived.We apply Washout filter to the neuron models to change the type of Hopf bifurcation,making subcritical Hopf bifurcation convert to supercritical Hopf bifurcation,thus obtaining different firing features of neurons.Secondly,an adaptive model of single neuron is established under external electric field.It can be found that there are two mechanisms which can produce spike-frequency adaptation,that are adaptive current mechanism and dynamic threshold mechanism.By comparing the spike frequency curves of the two mechanisms,it is found that the adaptive current mechanism can shift the frequency curves to higher inputs without affecting its slope.However,the frequency curves under dynamic threshold mechanism are divergent with the slope descending.Furthermore,the adaptive neural network with small world characteristics under external electrical stimuli is established.The influence of the frequency and amplitude of the external stimuli and noise on the network adaptability are studied.We find that the size of the network,adding edge probability and the coupling strength all have a certain degree of influence on the adaptability and information transmission of neural network.Thirdly,a method of fitting key parameters of neuron models based on neural firing properties is proposed.The traditional particle swarm optimization algorithm is improved.Based on the adaptive firing characteristics and the Parkinson’s state,three key parameters of adaptive model and thalamic model are fitted,separately.Using the fitted parameters to reconstruct the neuron model,the firing trajectories can be well predicted,and the validity of the fitting method is verified.Compared with the traditional particle swarm optimization algorithm,the advantages of the proposed algorithm are also verified.Finally,the sparse feedforward neural network is constructed to study the effect of excitability and inhibitory balance of neurons on the weak signal transmission of the network.It is found that increasing the excitation/ inhibition balance per layer reduce the requirement of dense/ strong connection of the neural network,which enhances the transmission performance of the signal in the weakly connected cortical network.It is proved that the background activity and the local excitation/ inhibition balance can co-select the signal transmission path.Furthermore,the mechanism of neuronal excitation/ inhibition balance in weak signal transmission is analyzed.The results of this thesis would provide theoretical bases to the coding mechanisms of neural information,diagnosis of mental disorders and electromagnetic stimulation mechanisms.