一类具比例时滞细胞神经网络的全局渐近稳定性  

Global Asymptotic Stability of a Class of Cellular Neural Networks with Proportional Delays

作　　者：周立群[1] 刘纪茹[1] 

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《工程数学学报》2013年第5期673-682,共10页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(60974144;61374009);天津市高等学校科技发展基金(20100813);天津师范大学博士基金(52LX34)~~

摘　　要：本文应用M-矩阵理论和构造合适的Lyapunov泛函,对具比例时滞细胞神经网络进行研究,得到确保该系统的平衡点存在唯一与全局渐近稳定的时滞依赖的充分条件.其次通过变换将这个系统等价变换成具常时滞与变系数的细胞神经网络,再通过M-矩阵理论和构造合适的Lyapunov泛函,得到确保该网络平衡点存在唯一与全局渐近稳定的时滞独立的充分条件.最后给出两个数值算例验证所得结果的正确性和与以往结果相比较低的保守性,并根据比例时滞因子的情况,分析了所得时滞依赖与时滞独立的条件的适用范围.By applying M-matrix theory and constructing suitable Lyapunov functional, we firstly discuss a class of cellular neural networks with proportional delays, and obtain a delaydependent sufficient condition for ensuring existence and uniqueness and global asymptotic stability of the system. Secondly, the system is transfromed into the cellular neural networks with constant delay and variable coefficients. A delay-independent sufficient condition is derived for ensuring existence and uniqueness and global asymptotic stability of the system by using M-matrix theory and constructing suitable Lyapunov functional again. Finally, two numerical examples are presented to verify the correctness of the numerical results and less conservative than the existing results, and the application scope of delay-dependent sufficient and delayindependent sufficient conditions according to the proportional delay factor are analyzed.

关 键 词：细胞神经网络 比例时滞因子 全局渐近稳定性 M-矩阵 LYAPUNOV泛函 

分 类 号：O175.13[理学—数学] TP183[理学—基础数学]