一类具比例时滞细胞神经网络概周期解的全局吸引性  

Global attractivity of almost periodic solutions for a class of cellular neural networks with proportional delays

作　　者：周立群[1] 赵山崎 

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《黑龙江大学自然科学学报》2014年第5期566-573,共8页Journal of Natural Science of Heilongjiang University

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

摘　　要：研究一类具比例时滞的二维分流抑制细胞神经网络的概周期解。应用Banach不动点定理,研究该网络的概周期解的存在性。通过一个非线性变换,将具比例时滞细胞神经网络等价地变换成具变系数与常时滞的细胞神经网络,通过构造合适的Lyapunov泛函并与Barbalat引理相结合,得到该网络概周期解存在唯一和全局吸引的充分条件。数值算例验证所得结论的正确性。Almost periodic solutions of two-dimensional shunting inhibitory cellular neural networks with proportional delays are studied. Firstly, the existence of almost periodic solutions of the networks is studied by applying Banach fixed point theorem. Secondly, a nonlinear transformation equivalently trans- forms the cellular neural networks with proportional delays into the cellular neural networks with constant delays and variable coefficients. By constructing suitable Lyapunov functional and applying Barbalat lem- ma, some sufficient conditions are derived for ensuring the existence and uniqueness and global attractivi- ty of almost periodic solutions for the system. Lastly, a numerical example is given to verify the correct- ness of the obtained conclusion.

关 键 词：细胞神经网络 概周期解 比例时滞 全局吸引性 Barbalat引理 

分 类 号：O175.13[理学—数学] TP183[理学—基础数学]