Synchronization Of Coupled Neuronal Network

In recent years,the synchronization dynamics of the coupled neuronal systems is an interesting topic.It is meaningful to study the synchronization behavior using biological neuronal network.This thesis,based on stochastic Hodgkin-Huxley equation,investigate the influences of network topology,synaptic delay and synaptic type on the firing patterns of neuronal systems.First of all,without the synaptic delay,the coupled inhibitory neuronal network poor synchronization and the firing rate decreases with the increase of the connection probability.In addition,as the intensity of membrane area increases,the network also becomes more and more out of sync,and the firing rate decreases.We further reveal that the presence of appropriate synaptic delay will facilitate the synchronization of the network.Secondly,we investigate the firing dynamics of the coupled excitatory neuronal net-work.Compared to the coupled inhibitory neuronal network,it occurs coherent firings.The firing rate increases as the connection probability increases.In addition,the pres-ence of an appropriate synaptic delay also facilitate the synchronization of the coupled excitatory neuronal network.thirdly,we investigate the firing behaviors of a neuronal network composed of both excitatory and inhibitory neurons.In the absence of synaptic delay,the network can occurs coherent firings.As the intensity of membrane area increases,the network also becomes more and more synchronized,but the firing rate decreases.Excitatory synapses can promote the synchronization of the networks,while inhibitory synapses can destroy inhibit the synchronization of the networks,but the influence of inhibitory synapses on the networks gradually becomes smaller with the increase of membrane area.For small membrane area,the presence of synaptic delay would have little effects on the synchronization of the networks;for moderate membrane area,the synaptic delay will cause the synchronized oscillation between the networks;as the membrane area is very large,the synchornization between the networks gets better and finally is stabilized,even the synaptic delay increases.In the end,we further investigation a network composed of two excitatory neuron clusters E1,E2 and an inhibitory neuron cluster I.We mainly study the impact of the network topology on the dynamics of such a neuronal network.For the case that the membrane area is large,the cluster E2 does accept inhibitory input and the cluster E1 and E2 do not form a loop,no synchronization is observed among three clusters;while for the case that the cluster E1 and E2 form a loop,there occur synchronized firings among the three clusters.