Boundedness and stability for Cohen–Grossberg neural network with time-varying delays.

*(English)*Zbl 1044.92001Summary: A model is considered to describe the dynamics of Cohen-Grossberg neural networks [M. A. Cohen and S. Grossberg, IEEE Trans. Syst. Man. Cybern. 13, 815–826 (1983; Zbl 0553.92009)] with variable coefficients and time-varying delays. Uniformly ultimate boundedness and uniform boundedness are studied for the model by utilizing the Hardy inequality. Combining with the Halanay inequality and the Lyapunov functional method, some new sufficient conditions are derived for the model to be globally exponentially stable. The activation functions are not assumed to be differentiable or strictly increasing. Moreover, no assumption on the symmetry of the connection matrices is necessary. These criteria are important in signal processing and design of networks.

##### MSC:

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

37N25 | Dynamical systems in biology |

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

68T05 | Learning and adaptive systems in artificial intelligence |

##### Keywords:

Ultimate boundedness; Lyapunov functional; Exponential stability; Hardy inequality; Halanay inequality; Cohen-Grossberg neural network
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\textit{J. Cao} and \textit{J. Liang}, J. Math. Anal. Appl. 296, No. 2, 665--685 (2004; Zbl 1044.92001)

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