Boundedness and global exponential stability for generalized Cohen–Grossberg neural networks with variable delay.

*(English)*Zbl 1090.92004Summary: A generalized Halanay inequality is established, and the boundedness of generalized Cohen-Grossberg neural networks [M. A. Cohen and S. Grossberg, IEEE Trans. Syst. Man Cybern. 13, 815–826 (1983; Zbl 0553.92009)] is investigated. By applying the generalized Halanay inequality and Lyapunov functional methods, new sufficient conditions are obtained ensuring the global exponential stability of solutions of generalized Cohen-Grossberg neural networks with variable delay. Three examples are also given for illustration.

##### MSC:

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

68T05 | Learning and adaptive systems in artificial intelligence |

34K20 | Stability theory of functional-differential equations |

34D23 | Global stability of solutions to ordinary differential equations |

34K60 | Qualitative investigation and simulation of models involving functional-differential equations |

##### Keywords:

Cohen-Grossberg neural networks; Global exponential stability; Halanay inequality; Dini derivative
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\textit{M. Jiang} et al., Appl. Math. Comput. 172, No. 1, 379--393 (2006; Zbl 1090.92004)

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##### References:

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