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Qualitative analysis of a neural network model with multiple time delays. (English) Zbl 1192.37115

Summary: We consider a simplified neural network model for a ring of four neurons where each neuron receives two time delayed inputs: One from itself and another from the previous neuron. Local stability analysis of the positive equilibrium leads to a characteristic equation containing products of four transcendental functions. By analyzing the equivalent system of four scalar transcendental equations, we obtain sufficient conditions for the linear stability of the positive equilibrium. Furthermore, we show that a Hopf bifurcation can occur when the positive equilibrium loses stability.

MSC:

37N25 Dynamical systems in biology
92B20 Neural networks for/in biological studies, artificial life and related topics
34K20 Stability theory of functional-differential equations
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