Global attraction and stability for Cohen-Grossberg neural networks with delays

Authors:
Kening Lu;Daoyi Xu;Zhichun Yang
Affiliations:
Department of Mathematics, Brigham Young University, Provo, UT 84602, USA;Institute of Mathematics, Sichuan University, Chengdu, 610064, PR China;Institute of Mathematics, Sichuan University, Chengdu, 610064, PR China
Venue:
Neural Networks
Year:
2006

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Abstract

We consider a class of Cohen-Grossberg neural networks with delays. We prove the existence and global asymptotic stability of an equilibrium point and estimate the region of existence. Furthermore, we show that the trajectories of the neural networks with positive initial data will stay in the positive region if the amplification function satisfies a divergent condition. We also establish the existence of a globally attracting compact set for more general networks. We estimate this compact set explicitly in terms of the network parameters from physiological and biological models. Our results can be applied to neural networks with a wide range of activation functions which are neither bounded nor globally Lipschitz continuous such as the Lotka-Volterra model. We also give some examples and simulations.