# zbMATH — the first resource for mathematics

Convergence and periodicity in a delayed network of neurons with threshold nonlinearity. (English) Zbl 1054.34112
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.

##### 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
Full Text: