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Bifurcation analysis for two coupled Fitzhugh-Nagumo neurons

In this paper, Hopf bifurcation in two coupled Fitzhugh-Nagumo (FHN) neurons is considered by applying the center manifold theorem. We learn that the condition for Hopf bifurcation is just sufficient but not necessary for the occurrence of a small limit cycle branched from a equilibrium. A stable limit cycle can branch from the equilibrium while its stability has no change. An equilibrium can only lose its stability in some particular directions in high dimensional phase space. Our analysis results indicate that saddle-node point seems to play a big part in the neurodynamics.