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Hopf bifurcation analysis in a synaptically coupled FHN neuron model with delays. (English) Zbl 1222.37097
Summary: We present an investigation of stability and Hopf bifurcation of the synaptically coupled nonidentical FHN model with two time delays. We first consider the existence of local Hopf bifurcations, by regarding the sum of the two delays as a parameter, then derive explicit formulas for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions, using the normal form method and center manifold theory. Finally, numerical simulations are carried out for supporting the theoretical analysis.
MSC:
37N25Dynamical systems in biology
92C20Neural biology
34K18Bifurcation theory of functional differential equations
34K20Stability theory of functional-differential equations
37G15Bifurcations of limit cycles and periodic orbits
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