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Global dynamic analysis of general Cohen-Grossberg neural networks with impulse. (English) Zbl 1142.34045
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)]. 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.

34K20Stability theory of functional-differential equations
34K45Functional-differential equations with impulses
37N25Dynamical systems in biology
92B20General theory of neural networks (mathematical biology)
Full Text: DOI
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