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Stability and Hopf bifurcation analysis on a ring of four neurons with delays. (English) Zbl 1175.34092

Authors’ abstract: We consider a four-neuron ring with self-feedback and delays. By analyzing the associated characteristic equation, linear stability is investigated and Hopf bifurcations are demonstrated, as well as the stability and direction of the Hopf bifurcation are determined by employing the normal form method and the center manifold reduction. Numerical simulations are presented to illustrate the results.

MSC:

34K18 Bifurcation theory of functional-differential equations
34K13 Periodic solutions to functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics

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References:

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