一类具一般功能反应的脉冲控制微分方程模型的非平凡周期解分支  

Bifurcation of nontrivial periodic solutions for impulsively controlled differential equation model with general functional responses

作　　者：刘华祥[1] 曾广洪[2] 

机构地区：[1]广东海洋大学数学系,广东湛江524088 [2]江西师范大学数学与信息科学学院,江西南昌330022

出　　处：《南昌大学学报（理科版）》2012年第5期429-434,共6页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金青年科学基金资助项目(61203153);江西师范大学科研计划资助项目(4556);广东海洋大学科研资助项目(0612163)

摘　　要：研究一类具一般功能反应的脉冲控制微分方程模型的非平凡周期解的形成问题。应用脉冲常微分方程的Floquet理论和比较方法证明了害虫绝灭解全局渐近稳定的条件;利用闪频映射的非平凡不动点方法证明了系统非平凡周期解分支的存在性。It investigates the occurrence of nontrivial periodic solutions for an impulsively controlled differential equation model with general functional responses.The Floquet theory and comparison techniques for impulsive ordinary differential equations is employed to obtain the sufficient conditions for the local asymptotic stability and the global asymptotic stability of the prey-eradication periodic solution.The problem of finding nontrivial periodic solutions is reduced to showing the existence of nontrivial fixed points for the associated stroboscopic mapping of time snapshot equal to the common period of controls.

关 键 词：脉冲控制 微分方程模型 非平凡周期解 分支 频闪映射 不动点方法 

分 类 号：O175.13[理学—数学]