發(fā)布時(shí)間：2018-07-29 08:12

【摘要】：眾所周知,科學(xué)技術(shù)突飛猛進(jìn)不但提高了經(jīng)濟(jì)的發(fā)展而且提高了人類生活的水準(zhǔn),但是環(huán)境問題卻變得嚴(yán)峻。特別是隨著工業(yè)生產(chǎn)的快速發(fā)展,進(jìn)一步加劇了環(huán)境的污染,如果不采取及時(shí)有效的措施,生物種群的生存環(huán)境將會(huì)受到嚴(yán)重的影響。種群生態(tài)學(xué)對(duì)人們的日常生產(chǎn)實(shí)踐具有重要的指導(dǎo)作用以及現(xiàn)實(shí)意義。特別是隨著環(huán)境的日益惡化,許多人對(duì)于種群在污染環(huán)境下生存狀況的研究一直是熱點(diǎn)問題。然而許多種群模型的研究?jī)H僅考慮把種群的成長(zhǎng)過程看成一個(gè)整體,這是不合理的。一方面：種群個(gè)體的每一個(gè)生命階段表現(xiàn)出的生理功能差異比較明顯；另一方面：不同階段的種群之間在生存時(shí)相互有影響。以上兩方面對(duì)種群的生存狀況具有重要的影響。因此,研究種群模型有必要考慮其生理階段的存在。所以,對(duì)于環(huán)境污染下的種群生存狀況研究,就需要我們通過建立合理的生物數(shù)學(xué)模型,并對(duì)種群模型進(jìn)行定性分析,預(yù)測(cè)種群在環(huán)境污染下的發(fā)展變化,這樣不僅可以制定相應(yīng)的環(huán)保措施使得種群可以持續(xù)生存,還對(duì)保持生態(tài)種群豐富的多樣性具有重要意義。論文的主要內(nèi)容結(jié)構(gòu)有以下幾個(gè)部分構(gòu)成：緒論第一章：預(yù)備知識(shí)。第二章：考慮了單種群兩階段(成年、幼年)的生物種群模型,其中成年和幼年種群同時(shí)受毒素影響。借助常微分方程相關(guān)理論方法,證明種群模型解有界、正平衡點(diǎn)和原點(diǎn)的穩(wěn)定性,然后給出了種群持續(xù)生存、滅絕的條件,又證明了種群模型有周期解并且是穩(wěn)定,最后運(yùn)用Matlab數(shù)值模擬證明了相關(guān)結(jié)論。第三章：考慮了具有種間相互作用的單種群兩階段生物種群模型,而且它們同時(shí)受毒素作用,證明了正解的有界性,平衡點(diǎn)的存在性和穩(wěn)定性,獲得了種群滅絕、生存的條件,同時(shí)考慮了周期解的相關(guān)結(jié)果。并數(shù)值模擬驗(yàn)證本章的結(jié)論。第四章：考慮了毒素影響下食餌-捕食數(shù)學(xué)模型(食餌是具有階段結(jié)構(gòu),捕食種群僅捕食幼年種群),得到了系統(tǒng)解的有界性,系統(tǒng)持久性的條件,并給出了系統(tǒng)周期解的存在性和穩(wěn)定性,最后通過數(shù)值模擬進(jìn)一步證明了文中的相關(guān)結(jié)論。第五章：考慮毒素作用下種群模型具有階段性和自食(捕食種群有階段性且自食),探討了食餌一捕食者模型持續(xù)生存問題以及周期解的相關(guān)結(jié)果,最后通過數(shù)值模擬進(jìn)一步證明了本章中的相關(guān)結(jié)論。最后,主要對(duì)論文進(jìn)行小結(jié)并提出未來需要進(jìn)一步討論的方向；致謝；參考文獻(xiàn)等。
[Abstract]:As we all know, the rapid development of science and technology has not only improved the economic development but also improved the standard of human life, but the environmental problems have become serious. Especially with the rapid development of industrial production, the pollution of the environment is further aggravated. If no timely and effective measures are taken, the living environment of the biological population will be seriously affected. Population ecology plays an important role in guiding people's daily production practice as well as practical significance. Especially with the deterioration of the environment, many people's research on the survival of the population in the polluted environment has been a hot issue. However, it is unreasonable for many population models to consider the population growth process as a whole. On the one hand, the difference of physiological function in each stage of the population is obvious; on the other hand, the different stages of the population affect each other in survival. The above two aspects have an important effect on the survival of the population. Therefore, it is necessary to consider the existence of physiological stage in the study of population model. Therefore, for the study of population survival under environmental pollution, we need to establish a reasonable biological mathematical model and qualitatively analyze the population model to predict the population development and change under environmental pollution. In this way, not only can the corresponding environmental protection measures be formulated to make the population survive sustainably, but also it is of great significance to maintain the rich diversity of the ecological population. The main content structure of the thesis has the following parts: the first chapter: preparatory knowledge. In chapter 2, a two-stage biological population model is considered, in which both adult and juvenile populations are affected by toxins. With the help of the theory of ordinary differential equation, it is proved that the solution of population model is bounded, and the stability of positive equilibrium point and origin point is proved. Then, the conditions of population survival and extinction are given, and it is proved that the population model has periodic solution and is stable. Finally, Matlab numerical simulation is used to prove the relevant conclusions. In chapter 3, the two-stage population model of single population with interspecific interaction is considered, and they are simultaneously affected by toxins. The boundedness of positive solution, the existence and stability of equilibrium point are proved, and the conditions for population extinction and survival are obtained. At the same time, we consider the results of periodic solutions. The conclusion of this chapter is verified by numerical simulation. In chapter 4, the predator-prey mathematical model under the influence of toxin is considered. The boundedness of the system solution and the condition of the persistence of the system are obtained. The existence and stability of the periodic solution of the system are given, and the relevant conclusions are further proved by numerical simulation. Chapter 5: considering that the population model has stages and self-feeding (prey population has stage and self-feeding) under the action of toxin, the problem of persistent survival of predator-prey model and the results of periodic solution are discussed. Finally, the relevant conclusions in this chapter are further proved by numerical simulation. Finally, the paper is summarized and the future direction of further discussion is put forward; thanks; references, etc.
【學(xué)位授予單位】：蘭州交通大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O175

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