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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:
34K18Bifurcation theory of functional differential equations
34K13Periodic solutions of functional differential equations
92B20General theory of neural networks (mathematical biology)
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