Wei, Junjie; Jiang, Weihua Stability and bifurcation analysis in a neural network model with delays. (English) Zbl 1099.34069 Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 13, No. 2, 177-192 (2006). 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 \(r=\sum_{j=1}^n \tau_j / n\). Reviewer: Pedro J. Torres (Granada) Cited in 4 Documents 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 Keywords:neural network; delay; stability; bifurcation PDFBibTeX XMLCite \textit{J. Wei} and \textit{W. Jiang}, Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 13, No. 2, 177--192 (2006; Zbl 1099.34069)