Synchronized Firings in the Networks of Class 1 Excitable Neurons with Excitatory and Inhibitory Connections and Their Dependences on the Forms of Interactions

Synchronized firings in the networks of class 1 excitable neurons with excitatory and inhibitory connections are investigated, and their dependences on the forms of interactions are analyzed. As the forms of interactions, we treat the double exponential coupling and the interactions derived from it: pulse coupling, exponential coupling, and alpha coupling. It is found that the bifurcation structure of the networks depends mainly on the decay time of the synaptic interaction and the effect of the rise time is smaller than that of the decay time.