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Zbl 1185.37204
Yu, Wenwu; Cao, Jinde
Stability and Hopf bifurcation on a two-neuron system with time delay in the frequency domain. (English)
[J] Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 4, 1355-1366 (2007). ISSN 0218-1274

Summary: A general two-neuron model with time delay is considered, where the time delay is regarded as a parameter. It is found that Hopf bifurcations occur when this delay passes through a sequence of critical value. By analyzing the characteristic equation and using the frequency domain approach, the existence of Hopf bifurcation is established. The stability of bifurcating periodic solutions is determined by the harmonic balance approach, the Nyquist criterion and a Hopf bifurcation graphical analysis. Numerical results are given to justify the theoretical analysis.

MSC 2000:: *37N25 Dynamical systems in biology
34K18 Bifurcation theory of functional differential equations
34K20 Stability theory of functional-differential equations
92C20 Neural biology

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Zentralblatt MATH Berlin [Germany]