Nonlinear Stochastic Dynamics Of Neuron And Its Network System

Neuron,with complex nonlinear characteristics,is the basic unit of brain neuron system,and its discharge pattern presents colorful dynamic behaviors.In this thesis,firstly the neuron and its network system based on key neural circuits and micro-neural networks were constructed.Then through stochastic simulation and nonlinear dynamic analysis,we studied the effects of intrinsic and extrinsic factors(such as noise,coupling mode,network topology,etc.)on the nonlinear dynamic characteristics(such as discharge mode,information coding,energy efficiency,etc.)of the complex neuron system.Finally using phase analysis and other methods to explore internal dynamics of neuron system,and so as to explain the possible internal mechanisms of neurodegenerative diseases or cognitive behaviors.The following research results have been achieved:(1)For the nonlinear dynamic characteristics of neuron systems,the firing mode regulation and phase synchronization were studied in the coupled neurons.First,the coupled FitHugh-Nagumo neuron model with time delay and noise was established,then the synchronization manifold of coupled neurons was derived theoretically.Finally,the effects of single time delay and multiple time delays on the discharge mode regulation and phase synchronization of the coupled neuron system were discussed.The results show that in single time delay or close multiple delay time,without noise,the neuronal system has a completely synchronized periodic discharge state of small amplitude and large amplitude alternately.With noise,the dynamic features of two neurons undergo a succession of transitions,the total synchronization?out-of-phase?alternating phase-drift and anti-phase state?anti-phase state.When one of time delay is largely dominant over the other,two neurons are at quiescent state without noise,and adding noise can change the neurons' state from the quiescent state to out-of-phase state.(2)The relationship between the neural discharge mode and energy was studied.First,the dependence of neuron on energy was derived theoretically under the high-low frequency signal,then the influences of energy absorption and release on the neural discharge pattern's transformation was discussed.The results show that high-low frequency signal induce more complicated discharge patterns.The energy absorption and release depend on the form of external stimulation and the transformation of neuron discharge pattern,as well as the response of electrical activity and Hamiltonian energy largely depend on change of periodic signal amplitude.The neuron systems'energy in multi-pattern state is lower than that of the periodic discharge state.(3)On the basis of above research,stochastic dynamic mechanism of neuron network was explored deeply.First,based on Hodgkin-Huxley neuron model,the mathematical model for encoding and transmitting sub-threshold excitatory postsynaptic signal was established in multilayer feed-forward neural network,then the propagation mechanism of weak signal was studied in multi-layer feed-forward neural network.The results show that the presence of background noise benefit the propagation speed of weak signal,and there exists an optimal area of background noise and synaptic weight at which the propagation speed and stability of weak signal can be enhanced.The speed of neuron information coding and signal transmission's fidelity can be increased,and delay time between the system and weak signal can be shorten.(4)The inhibition effect in discharge of neuron network system,that is,the inverse stochastic resonance(ISR),was studied.First,the mathematical model of neuronal network driven by Gaussian/non-Gaussian noise was established,then combined with the ISR observed in biological experiments,the conditions for ISR phenomenon caused by Gaussian/non-Gaussian colored noise were discussed.The results show that under the Gaussian colored noise,the occurrence and continuous conditions of ISR phenomenon depend on low external current,low cross-correlation rate and low noise level.Under the non-Gaussian color noise,the occurrence and continuous conditions of ISR phenomenon depend on low external current stimulation,and it generally exists the conditions of low noise correlation time or the departure of non-Gaussian noise.At the same time,the ISR phenomenon in neuron network shows more obvious and lasts longer than that of single neuron.(5)Finally,the periodic firing rate oscillation and cluster synchronization phenomena were studied in neural network.First,based on the adaptive index Integrate-and-Fire neuron model,the neural network model driven by different coupling forms was established,then the effects of electrical coupling or inhibitory/excitatory chemical coupling on periodic firing rate oscillation and cluster synchronization were discussed.The results show that the phenomenon of periodic firing rate oscillation in neural network is universal,and it occurs because the neurons in the network have cluster synchronization behaviors in different states.The neurons in the network will automatically be divided into two clusters,and firing state of neurons in each cluster is exactly same.The generation of cluster synchronization depends on delay time,and the neurons in different cluster states can change to each other with the change of delay time.