【摘要】：本論文主要研究了斑塊環(huán)境下兩類具有Beddington-DeAngelis功能反應(yīng)函數(shù)和時(shí)滯的捕食者-食餌模型.首先,介紹了有關(guān)的背景知識(shí)和一些預(yù)備知識(shí).其次,考慮了斑塊環(huán)境下具有單一捕食者的捕食者-食餌模型,通過(guò)構(gòu)造(1-函數(shù)的方法,借助已知的輔助系統(tǒng),利用比較定理,給出了具有單一捕食者的捕食者-食餌模型持久性和滅絕性的充分條件.接著考慮了斑塊環(huán)境下具有兩種捕食者的捕食者-食餌模型,考慮捕食者之間的競(jìng)爭(zhēng)關(guān)系,借助已知的輔助系統(tǒng),利用比較定理,給出了該捕食者-食餌系統(tǒng)的持久性的充分條件.并且借助龐加萊映射考慮了該捕食者-食餌模型的周期解的存在性.最后通過(guò)構(gòu)建適當(dāng)?shù)腖yapunov函數(shù)的方法得到了該系統(tǒng)存在唯一的全局漸近穩(wěn)定的正解.
[Abstract]:In this paper, two kinds of predator-prey models with Beddington-DeAngelis functional response function and time-delay in patch environment are studied. First, the background knowledge and some preparatory knowledge are introduced. Secondly, the predator-prey model with a single predator in patch environment is considered. By constructing (1-function), by means of the known auxiliary system, the comparison theorem is used. Sufficient conditions for permanence and extinction of predator-prey models with a single predator are given. Then considering the predator-prey model with two kinds of predators in patch environment, considering the competition between predators, and using the known auxiliary system, the comparison theorem is used. A sufficient condition for the permanence of the predator-prey system is given. The existence of periodic solutions of the predator-prey model is considered by means of the Poincare mapping. Finally, by constructing the appropriate Lyapunov function, we obtain the unique positive solution of the system with globally asymptotically stable.
【學(xué)位授予單位】：煙臺(tái)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175

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相關(guān)期刊論文 前2條

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本文編號(hào)：2311169