Some Of The Dynamic Behavior Of The Neurons And Their Networks

In this dissertation, the bifurcation behaviour of HR model and Chay model are studies through numerical simulation. The synchronization of two different excitable cell model are studies through Morris-Lecar (ML) model, but there not complete synchronization. The influences of noise and oscillator number to the synchronization of the network are studies through numerical simulation, using three indicators to describe the degree of synchronous behavior, such as the mean field, the synchronization factor and the firing probability. The results provide the theoretical basis for the application of noise and to achievement of the synchronization in the network.In Chapter 1, the goal and significance of this study, significance and development of the dynamics research in nervous system, significance and development of coupled neurons, studies coupled neurons in our national, as well as the content of this dissertation are introduced.In Chapter 2, some contents of basic theoretical knowledge are introduced, contents include the elementary concepts and knowledge of the excitable cell, types of types of synapses and their models, the knowledge of synchronization in dynamic system, the nonlinear elementary concepts corresponding to physiological experiment, bifurcation type in excitable system, the theory of stochastic resonance.In Chapter 3, Bifurcation behaviour of HR model and Chay model are studies through numerical simulation.In Chapter 4, the synchronization of two different excitable cell model are studies through numerical simulation, the effects of coupling strength on synchronization of electrically, the synchronization respect to the increase of coupling strength, but there not complete synchronization.In Chapter 5, The influences of noise and oscillator number to the synchronization of the network are studies through numerical simulation, using three indicators to describe the degree of synchronous behavior, such as the mean field, the synchronization factor and the firing probability. Three indicators increase firstly and then decrease with respect to the increase of noise density, implying that coherence resonance emerges. When the coupling strength and noise density are different, three synchronous indicators decrease with respect to the increase of oscillator number, indicating that the synchronous degree of the network becomes weaken with the increase of oscillator number.In Chapter 6, conclusion and discussion is provide.