Probably because this paper is in a rapidly developing area, at the intersection of applied mathematics and information science.

We do not think the methodology utilized in this paper is really a new discovery. Rather, Combing with the Halanay inequality, Hardy inequality, and the Lyapunov functional method, boundedness and stability of a class of non-autonomous Cohen-Grossberg networks is analyzed. The method used in this paper might be helpful when studying other non-autonomous dynamical systems.

The Cohen-Grossberg (C-G) neural network was firstly proposed by Cohen and Grossberg in 1983, it includes a lot of models from evolutionary theory, population biology, and neurobiology, and furthermore it encompasses the Hopfield neural network, cellular neural networks, and BAM networks as its special case. Earlier works done by many authors on the dynamics of C-G neural networks are about autonomous ones, whereas in this paper, some criteria are obtained ensuring the boundedness and stability of a class of non-autonomous C-G neural networks.

We were involved in this research because it is closely connected to our joint works with Jun Wang, Daniel W.C. Ho, Jinling Liang, and Xiaolin Li on the dynamical behavior of neural networks (Phys. Rev. E, 1999 and 2000; Physica D, 2004; IEEE Trans. Circuits Syst.-I, 2003, Neural Networks, 1998 and 2004; International Journal of Bifurcation and Chaos, 2004; Phys. Lett. A, 1999, 2000, 2001, and 2003). In these papers, different classes of neural networks are discussed, some analysis tools are utilized, and different forms of sufficient criteria are obtained. In addition, there also exist some recent works with Kun Yuan, Jun Wang, James Lam, Jinling Liang, Qingshan Liu, and Xiaolin Li on the stability analysis of delayed neural networks (IEEE Trans. Circuits Syst.-I, 2005, Physica D, 2005; IEEE Trans. Neural Networks, 2005,International Journal of Bifurcation and Chaos, 2005; Phys. Lett. A, 2005).

Our research is important in the design and application of neural networks, which could be used to solve some engineering problems such as signal processing, pattern recognition, associative memories, and optimization, etc. In addition, the methods given in this paper may be extended to more complex systems.