Bifurcations of FitzHugh-Nagumo excitable systems with chemical delayed coupling

Abstract

System of delayed differential equations is used to model a pairof FitzHugh-Nagumo excitable systems with time-delayed fastthreshold modulation coupling. The Hopf bifurcation of thestationary solution, due to coupling is completely described. Thecritical time delays, that include indirect and direct Hopfbifurcations, and conditions on the parameters for suchbifurcations are found. It is shown that there is a domain forvalues of time lags and coupling strength where instability of theequilibrium introduced by coupling can disappear due tointeraction delay.