时延细胞神经网络的全局渐近稳定性

Asymptotic stability of delayed cellular neural networks

通过构造新的Lyapunov泛函,在Lyapunov泛函中巧妙引入可调的实参数,并结合不等式运用的一些技巧,讨论了时延细胞神经网络的全局渐近稳定性问题,得到了该模型的平衡点全局渐近稳定的一些新的充分条件。所得的结果改进推广了已有文献中相应的一些结论,并且可应用于以前所不能处理的若干情形。理论分析和数学推导表明,全局渐近稳定性的一个简单充分判据与时延是有关的。所得结果突出了时延对于细胞神经网络的全局渐近稳定性的影响,这对于设计带时延的细胞神经网络有着重要的参考价值。此外,通过实例说明了相应结果的应用,这在理论上和应用中都有着重要的意义。

By constructing the new Lyapunov which can be adjusted, and making use of the inequa lular neural networks with variable coefficient was lities, the global asymptotic stability of delayed cel discussed and new sufficient conditions were ob tained. The results of this paper improve, extend, unify and complement a number of existing results. They also handle a number of cases not covered by known criteria. Theoretical analysis and mathemati- cal derivation show that the global asymptotic stability is related to the delay. The results we obtained highlight the impact of delay on the global asymptotic stability of cellular neural networks. This is of important guiding significance for the design of cellular neural networks with delay. Interesting exam- ples were included to show the versatility of our results. And they greatly enlarge the area of designing neural networks. This has important significance in both theory and application.