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Impulsive effects on stability of Cohen-Grossberg neural networks with variable delays. (English) Zbl 1103.34067
The authors analyze how the introduction of impulses into the continuous Cohen-Grossberg neural network with delays may affect its stability. Two questions arise: (i) Robustness of stability: whether the impulsive system remains stable when the original system is stable. (ii) Impulsive stabilization: whether the impulses are able to stabilize the original system when it is unstable. By means of two impulsive differential inequalities, sufficient conditions for the problems mentioned are given which improve and extend many previous stability criteria. These theoretical results are illustrated with a numerical study of two simple examples.
MSC:
34K20Stability theory of functional-differential equations
92B20General theory of neural networks (mathematical biology)
34K45Functional-differential equations with impulses