两类具有脉冲扩散的捕食—食饵模型的动力学分析

发布时间：2018-03-17 12:34

本文选题：捕食-食饵模型　切入点：周期解　出处：《信阳师范学院》2017年硕士论文　论文类型：学位论文

【摘要】：本文根据Lotka-Volterra捕食模型,通过构建Liapunov函数来研究正平衡点的全局渐近稳定性.该分析表明可以控制有关参数来实现食饵和捕食者的持续共存.在此模型的基础上引入外来种群,并通过固定时刻脉冲,建立了非线性脉冲入侵的捕食-食饵模型来分析物种间的关系.另外又研究了捕食者具有Allee效应的脉冲微分系统来分析本地物种与外来物种之间能共存条件.模型分析表明,通过脉冲条件来控制生物入侵或引进外来物种具有现实意义.根据外来物种的生长阶段特点,我们建立了入侵者是以Logistic方式增长的脉冲动力学模型.该模型主要利用弗洛盖定理和比较定理研究了周期解的全局渐近稳定性,可以用来为已经发生的生物入侵事件的控制策略提供指导.进而根据系统的持久性条件得出脉冲周期需要满足的一些条件,此脉冲周期也可以用于引进新的物种,以丰富物种数目,实现生物种群的多样性和谐共存.另外考虑捕食者受Allee效应的影响,建立了具有Allee效应的捕食系统模型.该模型主要分析了食饵灭绝周期解的全局渐近稳定性的条件,得出脉冲周期这一指标应满足的条件.这将为具有Allee效应的捕食系统的外来物种的管理提供重要的理论依据,并对有关管理部门的决策有参考指导作用.
[Abstract]:In this paper, the global asymptotic stability of positive equilibrium point is studied by constructing Liapunov function according to Lotka-Volterra predator model. The analysis shows that the parameters can be controlled to realize the continuous coexistence of prey and predator. On the basis of this model, the alien population is introduced. And through a fixed time pulse, A nonlinear prey-prey model with impulsive invasion is established to analyze the relationship between species, and the impulsive differential system with Allee effect is also studied to analyze the coexistence conditions between native species and alien species. It is of practical significance to control biological invasion or introduce alien species by pulse condition. In this paper, we establish a impulsive dynamic model in which intruders grow in the form of Logistic. In this model, the global asymptotic stability of periodic solutions is studied by using the Floogel theorem and the comparison theorem. It can be used to provide guidance for the control strategy of biological intrusion events that have already occurred. Then, according to the persistence conditions of the system, some conditions need to be satisfied with the pulse cycle, which can also be used to introduce new species. In order to enrich the number of species, the diversity of the species can coexist harmoniously. In addition, the predator is affected by the Allee effect. In this paper, a predator-prey system model with Allee effect is established, and the condition of global asymptotic stability of the periodic solution of prey extinction is analyzed. The condition of pulse period is obtained, which will provide an important theoretical basis for the management of alien species in predator-prey system with Allee effect, and can be used as a reference for the decision-making of relevant management departments.
【学位授予单位】：信阳师范学院
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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