The Phase Synchronization And Transition Progress Of Chay Neuronal Model

In this paper, we consider Chay neuronal model as an example. According to the Poincare’ mapping, we define the neuronal phase of spiking and bursting and use the numerical simulation to investigate the phase synchronization and its transition progress of two electrical coupled neurons and four types of regular coupled networks, whose parameters are not exactly the same.The second chapter studies the phase synchronization of two electrical coupling Chay neurons with the numerical methods. According to the bifurcation diagrams of IBIs and ISIs vs the coupling strength and the average frequency difference of bursting and spiking, we obtain the critical values of the coupling strength when the coupled neurons reach bursting and spiking synchronization under two different coupling parameters. In accordance with the time series of two neurons and the trajectories of two neurons in the V1-V2 plane before and after bursting and spiking synchronization, we describe the complex firing patterns and transition progress of two coupled neurons.The third chapter focuses on the phase synchronization of four coupled neurons with the chain, ring, star and global connections. We achieve the critical values of the coupling strength when the four connections reach bursting and spiking synchronization respectively. The conclusion is the same as the complete synchronization.The fourth chapter is a summary of the paper, which describes the main research contents, innovation and the existing deficiencies.