一类脉冲时滞微分方程的动力学分析  

Dynamic behavior of a class of impulsive delay differential equation

作　　者：邢苗苗[1] 蒋贵荣[1] 凌琳[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2015年第6期485-488,共4页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(11162004);广西自然科学基金(2012GXNSFAA053006);广西教育厅科研项目(KY2015YB112)

摘　　要：针对脉冲时滞微分方程周期解存在的充分性条件难于检验、难于求出周期解具体表达式等问题,构造Lyapunov泛函,利用全导数得到脉冲时滞微分方程零解一致渐近稳定的充分条件,给出了脉冲时滞微分方程的周期解和T-周期解、2T-周期解的显式表达式。周期解、初始值和不同时滞下方程解的数值结果验证了理论分析的正确性。In view of the difficulties in testing the sufficient conditions for the existence of periodic solutions and finding explicit periodic solutions, dynamic behavior of a class of impulsive delay differential equation is discussed. The sufficient conditions for uniformly asymptotically stability of trivial solutions are obtained by constructing Lyapunov funcational. Periodic solutions are discussed and the explicit solutions with period-T and period-2T are given. Numerical simulations on periodic solutions and solutions with different initial values and delays verify the theoretical analysis.

关 键 词：脉冲时滞微分方程 一致渐近稳定 周期解 

分 类 号：O175.1[理学—数学]