两种群均有收获率且食饵有群体防御能力的捕食系统  

A Prey-Predator System with Harvesting Rate for Preys and Predators while the Prey Population has Group Defense Ability

作　　者：段永红[1] 王万雄[1] 曹薇[2] 

机构地区：[1]兰州交通大学数理与软件工程学院,甘肃兰州730070 [2]西北师范大学数学与信息科学学院,甘肃兰州730070

出　　处：《贵州大学学报（自然科学版）》2008年第2期120-123,180,共5页Journal of Guizhou University:Natural Sciences

基　　金：国家自然科学基金();甘肃省自然科学基金()

摘　　要：对一类两种群均有收获率食饵种群具有群体防御能力且功能反应为I型的食饵种群系统进行了定性分析.得到奇点的稳定与全局稳定的一些性质.利用Liapunov函数和Poincare-Ben-dixson环域定理,得到了系统至少存在两个极限环的充分条件。Qualitative analysis of Ⅰ type function response predator-prey system with the harvesting rate for predator and prey which has group defense ability is studied in this paper. Some properties of the singular points of the system and its global ability are discussed. By utilizing the method of Liapunove function and Poincare-Bendixson theorem, the sufficient condition which the system has at least two limit cycles is obtained.

关 键 词：平衡点 稳定性 极限环 LIAPUNOV函数 Poincare-Bendixson环域定理 

分 类 号：O175.13[理学—数学]