Global asymptotic stability of Hopfield neural network involving distributed delays.

*(English)*Zbl 1082.68100Summary: We study dynamical behaviors of Hopfield neural networks system with distributed delays. Some new criteria ensuring the existence and uniqueness, and the global asymptotic stability (GAS) of equilibrium point are derived. In the results, we do not assume that the signal propagation functions satisfy the Lipschitz condition and do not require them to be bounded, differentiable or strictly increasing. Moreover, the symmetry of the connection matrix is not also necessary. Thus, we improve some previous works of other researchers. These conditions are presented in terms of system parameters and have importance leading significance in designs and applications of the GAS for Hopfield neural networks system with distributed delays. Two examples are also worked out to demonstrate the advantages of our results.

##### MSC:

68T05 | Learning and adaptive systems in artificial intelligence |

93D20 | Asymptotic stability in control theory |

##### Keywords:

Global asymptotic stability; Equilibrium point; Distributed delays; Hopfield neural networks
Full Text:
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