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Bifurcation analysis of a neural network model. (English) Zbl 0737.92001
Summary: This paper describes the analysis of the neural network model by H. R. Wilson and J. D. Cowan [Biophys. J. 12, 2-24 (1972)]. The neural network is modeled by a system of two ordinary differential equations that describe the evolution of average activities of excitatory and inbibitory populations of neurons. We analyze the dependence of the model’s behavior on two parameters. The parameter plane is partitioned into regions of equivalent behavior bounded by bifurcation curves, and the representative phase diagram is constructed for each region. This allows us to describe qualitatively the behavior of the model in each region and to predict changes in the model dynamics as parameters are varied.
In particular, we show that for some parameter values the system can exhibit long-period oscillations. A new type of dynamical behavior is also found when the system settles down either to a stationary state or to a limit cycle depending on the initial point.

92B20 Neural networks for/in biological studies, artificial life and related topics
34C23 Bifurcation theory for ordinary differential equations
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