一类捕食与被捕食系统的持续生存性与周期解  

Persistence and periodic orbits for a kind of predator prey system

作　　者：窦家维[1,2] 朱吉祥[1,2] 

机构地区：[1]西安联合大学师范学院数学系 [2]陕西师范大学数学系

出　　处：《陕西师大学报（自然科学版）》1997年第1期20-24,共5页Journal of Shaanxi Normal University(Natural Science Edition)

摘　　要：讨论了一类一个捕食者种群和两个食饵种群构成的非自治生态系统．系统中食饵种群有各自的避难所，它们在避难所内外可以迁移．应用常微分方程定性和稳定性的方法，得到了在一定条件下系统是持续生存的；进一步，若系统是一个周期系统，则在合适的条件下，系统存在唯一的。This paper considers a kind of nonautonomous system of one predator population and two prey populations, in which the prey populations can choose their own refuges to avoid being preyed by their natural enemy, and the prey species can diffuse between interior and exterior of the refuges. Using ordinary differential equation qualitative and stability method, it is proved that the system can be persistence under some conditions and that if the system is a periodic system, then it has a unige periodic solution, which is globally asymptotically stable under the appropriate conditions.

关 键 词：周期解 周期解 捕食者 被捕食者 种群 生态系统 

分 类 号：Q141[生物学—生态学] O175.12[生物学—普通生物学]