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Stability and bifurcation analysis in a neural network model with delays. (English) Zbl 1099.34069

The paper considers a neural network distributed in a ring with delays
\[ C\frac{du_j}{dt}=-\frac{1}{R_j}u_j+F(u_j(t-r))+G_j(u_{j-1}(t-\tau_{j-1})),\;j=1,\dots,n. \] The linear stability of the origin depends on the distribution of the roots of the characteristic equation. An analysis of such equation leads to new conditions on stability as well a Hopf bifurcation criterion in the special cases of \(r=0\) or \(r=\sum_{j=1}^n \tau_j / n\).

MSC:

34K20 Stability theory of functional-differential equations
34K18 Bifurcation theory of functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
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