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Zbl 1162.92002
Li, Kelin
Stability analysis for impulsive Cohen-Grossberg neural networks with time-varying delays and distributed delays. (English)
[J] Nonlinear Anal., Real World Appl. 10, No. 5, 2784-2798 (2009). ISSN 1468-1218

Summary: A class of impulsive {\it M. A. Cohen} and {\it S. Grossberg} [IEEE Trans. Syst. Man. Cybern. 13, 815--826 (1983; Zbl 0553.92009)] neural networks with time-varying delays and distributed delays is investigated. By establishing an integro-differential inequality with impulsive initial conditions, employing $M$-matrix theory and a nonlinear measure approach, some new sufficient conditions ensuring the existence, uniqueness, global exponential stability and global robust exponential stability of equilibrium points for impulsive Cohen-Grossberg neural networks with time-varying delays and distributed delays are obtained. In particular, a more precise estimate of the exponential convergence rate is provided. By comparisons and examples, it is shown that the results obtained here can extremely extend and improve previously known results.

MSC 2000:: *92B20 General theory of neural networks
34K20 Stability theory of functional-differential equations
34K45 Equations with impulses
34K60 Applications of functional-differential equations
68T05 Learning and adaptive systems

Keywords: impulses; delay; integro-differential inequality; Cohen-Grossberg neural networks; stability

Citations: Zbl 0553.92009

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