Effect of Topological Connectivity on Firing Pattern Transitions in Coupled Neurons

Abstract

By using the coupled model of Hindmarsh—Rose neuronal systems, we numerically investigate the effect of topology structures on the firing patterns transition (FPT). A four-cell coupled system with all possible configurations are studied. We select the membrane current Iext as a controllable parameter, and set it to be near the left side for one of the bifurcation points. It is found that to have a response from some external stimuli with the proper amplitude and frequencies, the transition will appear between different firing states only when the cells in the system are coupled with some proper topological structures, which implies the occurrence of FPT induced by the configuration in the coupled system. Similar FPT phenomena could also be observed in a five-cell coupled system. Furthermore, we find that such transition behaviors may have some inherent relevance with the synchronization error and the average connective number among cells in the coupled system for different topology structures. These results suggest that the biological neuron systems may achieve an effective response to the external feeble stimulus by selecting the proper configuration and using the corresponding transition mode.