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Zbl 1142.34045
Chen, Zhang; Ruan, Jiong
Global dynamic analysis of general Cohen-Grossberg neural networks with impulse. (English)
[J] Chaos Solitons Fractals 32, No. 5, 1830-1837 (2007). ISSN 0960-0779

This paper is concerned with the global exponential stability of an impulsive version of the Cohen-Grossberg neural networks model [{\it M. Cohen} and {\it S. Grossberg}, IEEE Trans. Syst. Man. Cybern. 13, 815--826 (1993; Zbl 0553.92009)]. \par More precisely, the authors consider the following problem $$\multline\frac{dx(t)}{dt}=-a_i(x_i(t))\left[b_i(x_i(t))-\sum_{j=1}^nc_{ij}f_j(x_i(t))\right. \\\left. -\sum_{j=1}^n \int_0^{+\infty}g_j(x_j(t-\tau_{ij}(t)-s)d_sK_{ij}(s)+I_i\right],\ t\not=t_k,\endmultline$$ $$x_i(t_k^+)-x_i(t_k)=I_{ik}(x_i(t_k)),\ t=t_k.$$ The principal result of this paper is based on the method of Lyapunov function. Several consequences are given.
[Abdelghani Ouahab (Sidi Bel Abbes)]

MSC 2000:: *34K20 Stability theory of functional-differential equations
34K45 Equations with impulses
37N25 Dynamical systems in biology
92B20 General theory of neural networks

Keywords: impulsive differential equation; neural networks model; stability; equilibrium point; Lyapunov function

Citations: Zbl 0553.92009

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