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Stability analysis for impulsive Cohen-Grossberg neural networks with time-varying delays and distributed delays. (English) Zbl 1162.92002

Summary: A class of impulsive M. A. Cohen and 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:

92B20 Neural networks for/in biological studies, artificial life and related topics
34K20 Stability theory of functional-differential equations
34K45 Functional-differential equations with impulses
34K60 Qualitative investigation and simulation of models involving functional-differential equations
68T05 Learning and adaptive systems in artificial intelligence

Citations:

Zbl 0553.92009
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References:

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