两种群食饵捕食系统的定性分析

【作者】 李锋；

【导师】 窦霁虹；

【作者基本信息】 西北大学 ， 基础数学， 2006， 硕士

【摘要】 本文讨论了两种群的食饵捕食系统。在第一章里介绍了两种群的食饵捕食系统的研究现状及研究意义。第二章研究了一类食饵—捕食者系统当食饵种群的增长率和捕食率都为非线性情形的定性行为,分析了该系统的平衡点的性态,给出了该系统极限环不存在、存在的充分条件,补充完善了程荣福、蔡淑云(2002)及颜向平、张存华(2004)的结论。第三章研究捕食者具有Beddington-Deangelis功能反应函数和周期脉冲扰动的捕食者-食饵系统,利用脉冲微分方程的Floquet理论和比较定理,得到了系统灭绝和持续生存的充分条件。在第四章里我们讨论了一个具有性别偏食的食饵捕食系统,得出了系统灭绝和一致持久的充分条件。并且利用重合度理论中的延拓定理,给出了周期解存在的充分条件,特别的,得到了具有性别偏食的自治的食饵捕食系统周期解存在的充分条件,补充了刘秀湘,冯佑和的结论。更多还原

【Abstract】 A kind of food-predator system are considered in this paper. Some background knowledge and the state of study are introduced in the first chapter. Based on the fact, the predator-prey system with functional response are considered, the quality of the equilibrium is discussed, the conditions of the existence and the nonexistence of the limit cycle are provided, and the conclusions of Cheng Rongfu and Yan Tonghua are bettered in the second chapter. The predator-prey system with Beddington-Deangelis functional response and periodic impulsive perturbations on the predator are considered by using the floquet theory of impulsive equation and comparison theorem, sufficient conditions for the system to be extinct and permanence are given in the third chapter. A prey-predator system with sexual favoritism are considered by means of a continuous theorem of coincidence degree theory, a sufficient condition of existence for periodic solution is presented in the fourth chapter. Especially, a sufficient condition of existence for periodic solution for automatic system is given out. The conclusions of Xiuixiang Liu and Youhe Feng are developed.更多还原