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Zbl 1092.34563
Li, Shaowen; Liao, Xiaofeng; Li, Chunguang; Wong, Kwok-Wo
Hopf bifurcation of a two-neuron network with different discrete time delays. (English)
[J] Int. J. Bifurcation Chaos Appl. Sci. Eng. 15, No. 5, 1589-1601 (2005). ISSN 0218-1274

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 2000:: *34K18 Bifurcation theory of functional differential equations
37G15 Bifurcations of limit cycles and periodic orbits
37N25 Dynamical systems in biology
92C20 Neural biology

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