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Global exponential stability in DCNNs with distributed delays and unbounded activations. (English) Zbl 1123.45006
The author obtains sufficient conditions under which the equilibrium \(x^*\) of the network \[ \frac{dx_i(t)}{dt}=-a_i x_i(t)+\sum_{j=1}^m b_{ij} f_j(x_j(t))+ \sum_{j=1}^m c_{ij}f_j \left(\int_0^\infty K_{ij}(s)x_j(t-s)\,ds\right)+I_i,\quad t>0, \] where \(i\in\{1,2,\dots,m\}\), is unique and globally exponentially stable.
Examples added with computer simulations are given to support the results obtained.

MSC:
45J05 Integro-ordinary differential equations
45M10 Stability theory for integral equations
92B20 Neural networks for/in biological studies, artificial life and related topics
93D30 Lyapunov and storage functions
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