## 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

Zbl 0553.92009
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