一类时滞微分系统的周期解  

Periodic Solutions for a Class of Delay Differential Systems

作　　者：刘可为[1] 王晓莉[1] 王晓佳[1] 

机构地区：[1]合肥工业大学数学学院,安徽合肥230009

出　　处：《大学数学》2012年第1期84-89,共6页College Mathematics

基　　金：合肥工业大学校基金(2009HGXJ0057;2010HGXJ0082)

摘　　要：研究了一类具分布时滞的一阶微分系统的周期解的存在性和全局吸引性.先通过利用重合度理论中的Mawhin延拓定理讨论了周期解的存在性,建立了一些判断准则;进而通过构造适当的Lyapunov泛函以及周期解的存在性结果研究了该类时滞微分系统的周期解的全局吸引性,获得了保证其周期解全局吸引的充分性条件.The existence and global attractivity of periodic solution for a class of one order differential systems with distributed delay are studied. By using Mawhin＇ s continuation theorem of coincidence degree theory, the existence of periodic solutions for the delay differential systems is discussed. Some criteria are established. Further, by constructing a proper Lyapunov functional and using the result of the existence of periodic solutions, the global attractivity of periodic solution for above systems are studied. And a sufficient condition to assure the global attractivity of periodic solution is obtained.

关 键 词：时滞 微分系统 周期解 延拓定理 全局吸引 

分 类 号：O175.14[理学—数学]