Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses.

*(English)*Zbl 1152.34343Summary: In this paper, by using the contraction principle and Gronwall-Bellman’s inequality, some sufficient conditions are obtained for checking the existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks (SICNNs) with impulse. Our results are essentially new. It is the first time that the existence of almost periodic solutions for the impulsive neural networks are obtained.

##### MSC:

34C27 | Almost and pseudo-almost periodic solutions to ordinary differential equations |

34A37 | Ordinary differential equations with impulses |

34D20 | Stability of solutions to ordinary differential equations |

37N25 | Dynamical systems in biology |

82C32 | Neural nets applied to problems in time-dependent statistical mechanics |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

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\textit{Y. Xia} et al., Chaos Solitons Fractals 34, No. 5, 1599--1607 (2007; Zbl 1152.34343)

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##### References:

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