两种群多时滞Lotka-volterra系统正周期解的存在性与吸引性  

The Existence and Global Attractivity of Positive Periodic Solutions of a Two-species Lotka-volterra System with Multiple Delays

作　　者：刘志军[1] 

机构地区：[1]湖北民族学院理学院,湖北恩施445000

出　　处：《湖北民族学院学报（自然科学版）》2008年第3期312-320,共9页Journal of Hubei Minzu University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10671001);湖北省高等学校创新团队基金资助项目(T200804);湖北省教育厅科学技术研究重点项目(B20082905);湖北省教育厅科学技术研究中青年基金项目(Q20082906)

摘　　要：对已经获得的关于具有周期系数的两种群多时滞Lotka-volterra系统正周期解的存在性和稳定性结果进行了归纳总结.在上述研究中,借助Mawhin拓扑度方法和Liapunov函数技巧,分别建立了竞争系统,捕食系统和互惠系统正周期解存在且全局吸引的充分条件,发现这些条件能够与对应的自治系统正平衡点的存在性和稳定性条件较好的对应起来,而且发现时滞对系统的渐近行为是有影响的.In this paper, we make a summary of some results on the existence and global attractivity of positive periodic solutions of a multi - delayed two - species Lotka - voherra system including competitire, predator- prey and facuhative forms. In the above research, by using Mawhin＇s continuous theorem and liapunov function, sufficient conditions for the existence and global attractivity of positive periodic solutions of the above three systems are derived, respectively. These results show that they can formally correspond to that of positive equilibrium of autonomous undelayed systems, respectively. Moreover, these results indicate that the periodic delays have effect on the asymptotic behaviors of systems.

关 键 词：LOTKA-VOLTERRA系统 时滞 正周期解 存在性 全局吸引性 

分 类 号：O174.14[理学—数学]