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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.
92B20General theory of neural networks (mathematical biology)
34K20Stability theory of functional-differential equations
34K45Functional-differential equations with impulses
34K60Qualitative investigation and simulation of models
68T05Learning and adaptive systems