Synchronization of coupled Hindmarsh-Rose neurons: Effects of an exogenous parameter*

Systems that show patterns or cycles are found throughout nature. The existence of interaction mechanisms among these systems may generate an overall new collective dynamic behavior such as synchronization. But not only may the interconnection among systems lead to synchronization, also the influences of the environment plays an important role in the stablishment of collective behavior. In this paper we study how synchronization of two diffusively coupled Hindmarsh-Rose neurons is affected by an exogenous parameter. In particular, we investigate by means of numerical simulations how the threshold of the coupling strength that is needed to synchronize depends on the value of the exogenous parameter. For those values of the exogenous parameter for which the overall behavior of the two coupled neurons is periodic we perform a local stability analysis of the synchronous state.