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Zbl 1044.92001
Cao, Jinde; Liang, Jinling
Boundedness and stability for Cohen--Grossberg neural network with time-varying delays. (English)
[J] J. Math. Anal. Appl. 296, No. 2, 665-685 (2004). ISSN 0022-247X

Summary: A model is considered to describe the dynamics of Cohen-Grossberg neural networks [{\it M. A. Cohen} and {\it 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 2000:: *92B20 General theory of neural networks
37N25 Dynamical systems in biology
34D23 Global stability
68T05 Learning and adaptive systems

Keywords: Ultimate boundedness; Lyapunov functional; Exponential stability; Hardy inequality; Halanay inequality; Cohen-Grossberg neural network

Citations: Zbl 0553.92009

Cited in: Zbl 1057.92003

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