Exponential stability and existence of periodic solutions for a class of recurrent neural networks with delays  

时滞反馈神经网络模型的周期解的存在性和全局稳定性(英文)

作　　者：戴志娟[1,2] 

机构地区：[1]南京大学数学系 [2]扬州教育学院数学系,扬州225002

出　　处：《Journal of Southeast University(English Edition)》2006年第2期286-293,共8页东南大学学报（英文版）

摘　　要：Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays （RNNs） are studied. By employing the inequality α∏k=1^m bk^qk≤1/r ∑qkbk^r＋1/rα^r（α≥0,bk≥0,qk〉0,with ∑k=1^m qk=r-1,r≥1, constructing suitable Lyapunov r k=l k=l functions and applying the homeomorphism theory, a family of simple and new sufficient conditions are given ensuring the global exponential stability and the existence of periodic solutions of RNNs. The results extend and improve the results of earlier publications.研究了一类具有连续分布延时的反馈神经网络模型的周期解的存在性和全局稳定性.通过利用不等式a∏mk=1bkqk≤1r∑k=m1qkbkr+1rar(a≥0,bk≥0,qk>0,且∑km=1qk=r-1,r≥1,构造适当的Lyapunov函数,以及运用同构定理,得到了一系列简单有用的条件,推广并完善了已有结论.

关 键 词：recurrent neural network global exponential stability periodic solution delay HOMEOMORPHISM Lyapunov function 

分 类 号：O175[理学—数学]