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Bautin bifurcation analysis for synchronous solution of a coupled FHN neural system with delay. (English) Zbl 1221.34188
Summary: The Bautin bifurcation of synchronous solution of a coupled FHN neural system with delay is investigated. Firstly, the method of Lyapunov functional is used to obtain conditions for the synchronization of the neural system. Then, distributions of the roots of the characteristic equation associated with the linearization of the synchrosystem are discussed. Center manifold and normal form are employed to calculate its Lyapunov coefficients. A group of sufficient conditions are given to present Bautin bifurcation of the synchrosystem by applying the Bautin bifurcation theorem of delay differential equations developed by Anca-Veronica Ion. The Bautin bifurcation diagram in the physical parameter space is provided to illustrate the correctness of our theoretical analysis.
MSC:
34K18Bifurcation theory of functional differential equations
34K20Stability theory of functional-differential equations
37N25Dynamical systems in biology
92B20General theory of neural networks (mathematical biology)
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