Guo, Shangjiang; Huang, Lihong; Wu, Jianhong Convergence and periodicity in a delayed network of neurons with threshold nonlinearity. (English) Zbl 1054.34112 Electron. J. Differ. Equ. 2003, Paper No. 61, 14 p. (2003). The paper considers the model for an artificial neural network of two neurons \[ \dot x = -\mu x +a_{11} f(x(t-\tau))+a_{12} f(y(t-\tau)),\quad\dot y = -\mu y +a_{21} f(x(t-\tau))+a_{22} f(y(t-\tau)), \] with \(\mu>0\), \(\tau>0\), \(x,y\in \mathbb{R}\). The activation function \(f\) is assumed to be \(f(\xi)=-\delta\) for \(\xi>0\) and \(f(\xi)=\delta\) for \(\xi\leq 0\). The authors show that the model can be reduced to a one-dimensional map. As a result, a detailed analysis of the dynamics of the network starting from nonoscillatory states is presented. Reviewer: Sergiy Yanchuk (Berlin) Cited in 2 Documents MSC: 34K13 Periodic solutions to functional-differential equations 34K25 Asymptotic theory of functional-differential equations 92B20 Neural networks for/in biological studies, artificial life and related topics Keywords:neural networks; feedback; McCulloch-Pitts nonlinearity; one-dimensional map; periodic solution PDFBibTeX XMLCite \textit{S. Guo} et al., Electron. J. Differ. Equ. 2003, Paper No. 61, 14 p. (2003; Zbl 1054.34112) Full Text: EuDML EMIS