Burst Synchronization And Rhythm Dynamics In The Neuronal Network

Bursting is an important firing pattern of neurons, and burst synchroniza-tion is closely related to the information transmission between neurons. Med-ical facts have shown that abnormal synchronization of neurons is the main cause of nervous diseases. Therefore, this paper mainly investigates the effects of the coupling schemes, mixed bursting type and multi-level network topology on dynamics of the neuronal network by using nonlinear dynamics theory and method.Firstly, The effects of the network topology, coupling mode and coupling strength on the burst synchronization and rhythm dynamics in a small world neuronal network is studied. By introducing the width factor f, the bursting type of neurons is divided into two types-short bursting and long bursting. It is found that the burst synchronization of the electrically coupled neuronal network is easier to be realized, the bursting type of the neuronal network can be changed into short bursting from long bursting by increasing the value of the connection probability for larger coupling strength; While for chemically coupled neuronal network, the bursting type of the network will transit from short bursting to long bursting with the change of the connection probability or the coupling strength. But for the long bursting network, its type will not be changed.Further, we studied the dynamical properties of the neuronal networks with mixed bursting neurons, which is closely to the biological nervous system. In this part, we introduced a factor r-the ratio of short bursting neurons and long bursting neurons. It is found that when r=0.5, the bursting type of the network is short bursting in the electrically coupled neuronal network, and the network shows long bursting in the chemically coupled network. This suggests that the short bursting type is dominant in electrically coupled neuronal networks.Finally, we studied burst synchronization and rhythm dynamics of the two-layer neuronal networks. In this part, the initial bursting type of two layers of network are set to be different. It is concluded that synchronization is en-hanced by increasing the coupling strength or connection probability between sub-networks, and the bursting type of the chemically coupled neuronal net-work will eventually show long bursting. The study can not only promote the development of nonlinear dynamics, but also play a positive role for the treat-ment of some nervous diseases.