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Stability of Cohen-Grossberg neural networks with unbounded distributed delays. (English) Zbl 1137.34351
The paper deals with the following system, being referred to as Cohen-Grossberg neural network model with distributed delay: $$\multline\dot x_i(t)=-a_i(x_i(t)) \biggl( d_i(x_i(t))-\sum_{j=1}^n b_{ij} g_j(x_j(t)) -\sum_{j=1}^n c_{ij} \int_{-\infty^t} k_{ij}(t-s) g_j(x_j(s))\,ds\biggr), \\ x_i(t)=\varphi_i(t),\quad t\le 0,\quad i=1,\dots,n, \endmultline $$ where $\varphi_i$ is bounded and continuous on $(-\infty,0]$. For this system sufficient conditions for the stability of the equilibrium point are obtained. The result is based on the variation-of-constant formula and the comparison principle.

34K20Stability theory of functional-differential equations
92B20General theory of neural networks (mathematical biology)
Full Text: DOI
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