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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 |

### Keywords:

impulses; delay; integro-differential inequality; Cohen-Grossberg neural networks; stability### Citations:

Zbl 0553.92009
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\textit{K. Li}, Nonlinear Anal., Real World Appl. 10, No. 5, 2784--2798 (2009; Zbl 1162.92002)

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