本文選題：捕食-食餌模型　切入點：周期解　出處：《信陽師范學院》2017年碩士論文　論文類型：學位論文

【摘要】：本文根據(jù)Lotka-Volterra捕食模型,通過構(gòu)建Liapunov函數(shù)來研究正平衡點的全局漸近穩(wěn)定性.該分析表明可以控制有關(guān)參數(shù)來實現(xiàn)食餌和捕食者的持續(xù)共存.在此模型的基礎(chǔ)上引入外來種群,并通過固定時刻脈沖,建立了非線性脈沖入侵的捕食-食餌模型來分析物種間的關(guān)系.另外又研究了捕食者具有Allee效應(yīng)的脈沖微分系統(tǒng)來分析本地物種與外來物種之間能共存條件.模型分析表明,通過脈沖條件來控制生物入侵或引進外來物種具有現(xiàn)實意義.根據(jù)外來物種的生長階段特點,我們建立了入侵者是以Logistic方式增長的脈沖動力學模型.該模型主要利用弗洛蓋定理和比較定理研究了周期解的全局漸近穩(wěn)定性,可以用來為已經(jīng)發(fā)生的生物入侵事件的控制策略提供指導.進而根據(jù)系統(tǒng)的持久性條件得出脈沖周期需要滿足的一些條件,此脈沖周期也可以用于引進新的物種,以豐富物種數(shù)目,實現(xiàn)生物種群的多樣性和諧共存.另外考慮捕食者受Allee效應(yīng)的影響,建立了具有Allee效應(yīng)的捕食系統(tǒng)模型.該模型主要分析了食餌滅絕周期解的全局漸近穩(wěn)定性的條件,得出脈沖周期這一指標應(yīng)滿足的條件.這將為具有Allee效應(yīng)的捕食系統(tǒng)的外來物種的管理提供重要的理論依據(jù),并對有關(guān)管理部門的決策有參考指導作用.
[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.
【學位授予單位】：信陽師范學院
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175

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