Abstract

System of delayed differential equations is used to model a pair of FitzHugh-Nagumo excitable systems with time-delayed fast threshold modulation coupling. The Hopf bifurcation of the stationary solution, due to coupling is completely described. The critical time delays, that include indirect and direct Hopf bifurcations, and conditions on the parameters for such bifurcations are found. It is shown that there is a domain for values of time lags and coupling strength where instability of the equilibrium introduced by coupling can disappear due to interaction delay.

Keywords: Hopf bifurcation; delayed differential equations.

MSC: 34K18, 37N25

Pages:  103--114     

Volume  63 ,  Issue  2 ,  2011