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Global existence of periodic solutions in a simplified four-neuron BAM neural network model with multiple delays. (English) Zbl 1100.92015

Summary: We consider a simplified bidirectional associated memory (BAM) neural network model with four neurons and multiple time delays. The global existence of periodic solutions bifurcating from Hopf bifurcations is investigated by applying the global Hopf bifurcation theorem due to J. Wu [Trans. Am. Math. Soc. 350, No. 12, 4799–4838 (1998; Zbl 0905.34034)] and Bendixson’s criterion for high-dimensional ordinary differential equations due to Y. Li and J. S. Muldowney [ J. Differ. Equations 106, No. 1, 27–39 (1993; Zbl 0786.34033)]. It is shown that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of the sum of two delays. Numerical simulations supporting the theoretical analysis are also included.

MSC:

92C20 Neural biology
34C25 Periodic solutions to ordinary differential equations
37N25 Dynamical systems in biology
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References:

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