Fan, Dejun; Hong, Ling Hopf bifurcation analysis in a synaptically coupled FHN neuron model with delays. (English) Zbl 1222.37097 Commun. Nonlinear Sci. Numer. Simul. 15, No. 7, 1873-1886 (2010). 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. Cited in 15 Documents MSC: 37N25 Dynamical systems in biology 92C20 Neural biology 34K18 Bifurcation theory of functional-differential equations 34K20 Stability theory of functional-differential equations 37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems Keywords:FHN model; time delay; Hopf bifurcation; stability switch; periodic solutions PDFBibTeX XMLCite \textit{D. Fan} and \textit{L. Hong}, Commun. Nonlinear Sci. Numer. Simul. 15, No. 7, 1873--1886 (2010; Zbl 1222.37097) Full Text: DOI References: [1] Hodgkin, A. L.; Huxley, A. F., A quantitative description of membrane and its application to conduction and excitation in nerve, J Physiol, 117, 500-544 (1952) [2] FitzHugh, R., Impulses and physiological state in theoretical models of nerve membrane, Biophys J, 1, 445-466 (1961) [3] Nagumo, J.; Arimoto, S.; Yoshizawa, S., An active pulse transmission line simulating nerve axon, Proc IRE, 50, 2061-2070 (1962) [4] Bautin, A. 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