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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 [M. Cohen and S. Grossberg, IEEE Trans. Syst. Man. Cybern. 13, 815–826 (1993; Zbl 0553.92009)].

More precisely, the authors consider the following problem

dx(t) dt=-a i (x i (t))b i (x i (t))- j=1 n c ij f j (x i (t))- j=1 n 0 + g j (x j (t-τ ij (t)-s)d s K ij (s)+I i ,tt k ,
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.

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