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Zbl 1137.34351
Huang, Tingwen; Li, Chuandong; Chen, Goong
Stability of Cohen-Grossberg neural networks with unbounded distributed delays.
(English)
[J] Chaos Solitons Fractals 34, No. 3, 992-996 (2007). ISSN 0960-0779

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.
[Ivan Ginchev (Varese)]
MSC 2000:
*34K20 Stability theory of functional-differential equations
92B20 General theory of neural networks

Keywords: neural network models; delay functional differential equations; stability

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