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Hopf bifurcation of a two-neuron network with different discrete time delays. (English) Zbl 1092.34563
Summary: A two-neuron network with different time delays is investigated. By analyzing the associated characteristic equation, we obtain conditions for delay-dependent and delay-independent asymptotic stability, respectively. Furthermore, we find that if the delay is used as a bifurcation parameter, Hopf bifurcation would occur. The direction and stability of the bifurcating periodic solutions are determined by using the Nyquist criterion and the graphical Hopf bifurcation theorem. Some examples are included to illustrate our results.
MSC:
34K18Bifurcation theory of functional differential equations
37G15Bifurcations of limit cycles and periodic orbits
37N25Dynamical systems in biology
92C20Neural biology