本文選題：捕食模型 + 脈沖出生��； 參考：《山西師范大學(xué)》2015年碩士論文

【摘要】：本文研究了幾類具有脈沖作用的捕食模型的動(dòng)力學(xué)性質(zhì),全文共分為三章：第一章,緒論,介紹了本文的研究背景,主要工作以及所用到的預(yù)備知識.第二章：建立并研究了污染環(huán)境中具有脈沖出生和收獲的捕食模型,利用頻閃映射得到了捕食者滅絕周期解的充分條件.進(jìn)一步,討論了捕食者滅絕周期解的全局吸引性和系統(tǒng)的持久性,并得到了閾值條件.這些理論為保護(hù)種群免于在污染環(huán)境中滅絕提供了可靠的理論依據(jù).最后本章給出數(shù)值模擬來驗(yàn)證理論結(jié)果的正確性.第三章,建立并研究了具有脈沖擴(kuò)散和脈沖收獲的單種群模型.利用由頻閃映射得到的離散動(dòng)力學(xué)系統(tǒng),得到了一個(gè)正不動(dòng)點(diǎn)并且當(dāng)種群的捕獲量小于某一值或脈沖周期大于某一值時(shí)這個(gè)正不動(dòng)點(diǎn)是全局穩(wěn)定的.相應(yīng)地,這個(gè)具有脈沖擴(kuò)散和脈沖收獲的單種群系統(tǒng)有一個(gè)全局穩(wěn)定的正周期解.最后本章給出數(shù)值模擬來驗(yàn)證理論結(jié)果的正確性.第四章,建立并研究了一類具有B-D功能性反應(yīng)函數(shù)的捕食者有病的捕食模型,該模型考慮了基于食餌的一個(gè)固定比例的避難所,它為食餌提供了一個(gè)免于被捕食的生存環(huán)境.通過對系統(tǒng)的定性分析得到了模型平衡點(diǎn)的存在性與穩(wěn)定性的充分條件.進(jìn)一步：利用比較定理得到了系統(tǒng)持久性的充分條件.最后本章給出數(shù)值模擬來驗(yàn)證理論結(jié)果的正確性.
[Abstract]:In this paper, the dynamic properties of several predatory models with impulsive action are studied. The whole paper is divided into three chapters: chapter one, introduction. The background, main work and the preparatory knowledge used in this paper are introduced. Chapter 2: the predator model with impulsive birth and harvest in polluted environment is established and studied. The sufficient conditions for the periodic solution of predator extinction are obtained by stroboscopic mapping. Furthermore, the global attractiveness of the periodic solution of predator extinction and the permanence of the system are discussed, and the threshold conditions are obtained. These theories provide a reliable theoretical basis for protecting populations from extinction in polluted environment. Finally, numerical simulation is given to verify the correctness of the theoretical results. In chapter 3, a single population model with pulse diffusion and pulse harvesting is established and studied. Using the discrete dynamical system derived from stroboscopic mapping, a positive fixed point is obtained and the positive fixed point is globally stable when the population catch is less than a certain value or the pulse period is greater than a certain value. Accordingly, the single-species system with impulsive diffusion and impulsive harvesting has a globally stable positive periodic solution. Finally, numerical simulation is given to verify the correctness of the theoretical results. In chapter 4, a predator-diseased predator model with B-D functional response function is established and studied. The model considers a fixed-scale shelter based on prey, which provides a living environment free from prey. The sufficient conditions for the existence and stability of the equilibrium point of the model are obtained by qualitative analysis of the system. Furthermore, the sufficient conditions for the persistence of the system are obtained by using the comparison theorem. Finally, numerical simulation is given to verify the correctness of the theoretical results.
【學(xué)位授予單位】：山西師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 孫樹林;原存德;;捕食者具有流行病的捕食-被捕食(SI)模型的分析[J];生物數(shù)學(xué)學(xué)報(bào);2006年01期

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本文編號：1961200