Symmetry And Synchronization Analysis Of Cell Networks

Cells are believed to be the key elements in the signal processing of neural system. The transmitting of neural information exhibits nonlinear characteristics, so the dynamic performance of coupled neurons gets the main focus in the neuroscience research. Many cells coupling to form networks, transmitting information, and their interaction complete the neural work, the synchronization of coupled cells plays the main role in the process of neural information transmitting, and the symmetry of the cell network has a huge effect on the synchronization. In this paper, the network synchronization affected by symmetry is investigated.After studying the synchronization and stability of two symmetric coupled cells in this paper, it is found that, effected by the coupling parameter, one subsystem will change its former state and synchronize with the other subsystem. Because of the work of the coupling parameter, the change of the initial value of one subsystem would cause the whole system to change from one stable state to another.As for three-cell networks, they are first divided into five categories according to their symmetry: Z 3symmetry, D3 symmetry, Z 2symmetry, interior Z 2symmetry, none symmetry. According to the combination of the networks and the theory of information transmitting through one cell, the cable model and the mathematical model based on FHN model are established. The symmetric condition is found for local synchronization, independent of the coupling parameter; it also gives the sufficient condition of the coupling parameter for the kinds of networks to synchronize.The research proves the significant effect on synchronization from symmetry. The results of simulation demonstrate the validity of the theoretic analysis.