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Local stability and bifurcation in a three-unit delayed neural network. (English) Zbl 1037.34067

The authors study a three-unit network of neural cells with delayed coupling \[ \dot x_i(t)=-x_i(t)+\sum_{j=1}^3 a_{ij}\beta \tanh(x_j(t-\tau)), \quad i=1,2,3. \] They derive a general formula for the bifurcation direction (criticality) of the Hopf bifurcation and an asymptotic estimate on the period of the emanating periodic solution.

MSC:

34K18 Bifurcation theory of functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
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