食饵-捕食者两种群同时捕获模型的定性分析  

A Qualitative Analysis of Two Species Harvested Simultaneously for Prey-predator Model

作　　者：杨海霞[1] 兰晓晶[1] 孙志强[1] 

机构地区：[1]兰州交通大学数学系,甘肃兰州730070

出　　处：《盐城工学院学报（自然科学版）》2007年第4期7-9,共3页Journal of Yancheng Institute of Technology:Natural Science Edition

基　　金：国家自然科学基金(604730304);兰州交通大学青蓝人才工程基金资助计划资助(QL-05-18A)

摘　　要：对有密度制约的食饵-捕食者两种群同时进行捕获系统的奇点进行了定性分析,讨论了平衡点的存在性、稳定性及此系统极限环的不存在性。另为,对正平衡点的局部稳定性和全局稳定性进行了详细分析,并证明了系统在正平衡点处是全局稳定的。从生态学的角度对所得的结果作出了解释,为生物资源的实际开发与管理提供了必要的理论依据。从生态意义上得到了两种群持续生存的充分条件。This paper analyzes qualitative property of the equilibrium for a simultaneous harvest prey - predator systems with density - restriction , and carries out the existence and stability of equilibria and the nonexistence of limit cycle. In addition , local and global stability of the positive equilibrium point is analyzed in detail. We illustrates that positive equilibrium point of this system is globally stable. Biological significance of the results is presented too, which provides theoretical bases for the optimal harvesting and management of the renewable biological resources. Sufficient conditions of two species persistence are ecologically obtained.

关 键 词：食饵-捕食系统 平衡点 全局稳定性 

分 类 号：O175[理学—数学]