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

Campbell, Sue Ann; Ruan, Shigui; Wei, Junjie

Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, No. 8, 1585-1595 (1999).

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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