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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
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