Synchronization And Rhythm Dynamics Of A Small World Network Consisting Of Mixed Synapses

In the cognitive process of the human brain,the synchronization and rhythm dynamics of neuronal network is associated with information transmission and processing.The main activity of neurons is bursting,and bursting synchronization of network is closely related to information transmission between neurons.Thus,exploring burst synchronization and rhythm dynamics of neuronal network with different network topology,coupling mode,mixed bursting neurons and noise is significant.In chapter 1,burst synchronization and rhythm dynamics of a small-world neuronal network consisting of mixed bursting types of neurons coupled via inhibitory-excitatory chemical synapses are explored.A quantitative characteristic,the average width factor is used to characterize the rhythm dynamics of the neuronal network and the parameter of synchronization degree is calculated to measure the spiking of the neurons.Numerical results show that the ratio of the inhibitory synapses in the network is the major factor why we get a similarly bell-shaped dependence of synchronization,and why the average width factor of the network decreases.We also find that not only the increasing of the coupling strength can promote synchronization to some extent,but also adding the probability of random adding edges of the small-world,while the ratio of long bursting in the initial state has little effect on the burst synchronization and the average width factor of the network.At last,when changing the coupling strength of excitatory synapses or inhibitory synapses,the trends of the parameter of synchronization and the width factor don't change,while the curve of the parameter become much sharper.In chapter 2,synchronization and stochastic resonance of a small-world neuronal network with Gaussian noise coupled via inhibitory-excitatory chemical synapses are explored.Numerical results show that the strength of noise has little effect on the synchronization,which is still sensitive to the proportion of inhibitory synapses,coupling strength and the probability of adding edges.It's a striking phenomenon that when the proportion of inhibitory synapses is high,the synchronization of the network is bad unexpectedly.As for the stochastic resonance,there exit the best coupling strength and strength of noise by which the stochastic resonance of the network is maximal.At the same time,probability of adding edges and proportion of inhibitory synapses are another two parameters that will influence the degree of the stochastic resonance and the best coupling strength and strength of noise above.In the case of proper coupling strength and probability of adding edges,the stochastic resonance of the network will be best when the network is coupled totally by inhibitory synapses.