【摘要】：本文主要研究由珊瑚、海藻、食草魚和食肉魚類所組成的珊瑚礁生態(tài)系統(tǒng),通過分析它們之間的關(guān)系,我們建立了三個(gè)模型.第一個(gè)模型主要討論了大型食肉魚、食草魚、人類對(duì)兩種魚類的捕撈的相互關(guān)聯(lián)和影響,其中的創(chuàng)新性體現(xiàn)在對(duì)食草魚按年齡或體積大小進(jìn)行分類,針對(duì)某些參數(shù)取值范圍所得結(jié)論與發(fā)表在SCIENCE的文獻(xiàn)[P.Mumby,etc 40]數(shù)據(jù)吻合;第二個(gè)模型主要討論兩種食草魚與海藻之間的關(guān)系,其中定居魚(Damselfish)與海藻是互利共生關(guān)系,鸚嘴魚(Parrotfish)與海藻是捕食者和被捕食者關(guān)系,而定居魚與鸚嘴魚是競(jìng)爭(zhēng)關(guān)系,該模型的創(chuàng)新性體現(xiàn)在第一次把定居魚的作用考慮到珊瑚礁生態(tài)系統(tǒng)中,而大量實(shí)驗(yàn)數(shù)據(jù)表明定居魚對(duì)保持藻類的多樣性起到至關(guān)重要的作用,所以我們的模型能更好反應(yīng)珊瑚礁生態(tài)系統(tǒng)的實(shí)際情況,接著我們對(duì)模型的動(dòng)力學(xué)行為(正不變性、有界性、不動(dòng)點(diǎn)的穩(wěn)定性及其分支等)進(jìn)行了詳細(xì)研究并對(duì)給定參數(shù)后的系統(tǒng)做了數(shù)值模擬;第三個(gè)模型繼續(xù)討論海藻-定居魚-鸚嘴魚的關(guān)系,不同之處在于我們用May在1976年提出的協(xié)作模型來反映海藻與定居魚的協(xié)作關(guān)系,我們對(duì)系統(tǒng)的動(dòng)力學(xué)行為進(jìn)行了詳細(xì)研究并做了數(shù)值模擬.論文所用數(shù)學(xué)工具主要包括Hartman-Grobman定理、Routh-Hurwitz定理和Sotomayor不動(dòng)點(diǎn)分支定理.
[Abstract]:In this paper, the coral reef ecosystem consisting of coral, seaweed, grass carp and carnivorous fish is studied. By analyzing the relationship between them, we have established three models of coral reef ecosystem, which are composed of coral, seaweed, grass carp and carnivorous fish. The first model focuses on the interlinkages and impacts of large carnivorous fish, grass carp and humans on the fishing of two species of fish, the innovation of which is the classification of grass carp by age or size. The results obtained according to the range of some parameters agree with the data published in SCIENCE [P. Mumby, etc 40]. The second model mainly discusses the relationship between two species of grass carp and seaweed, in which settled fish (Damselfish) and seaweed are mutually beneficial symbiosis, parrotfish (Parrotfish) and seaweed are predators and arrested predators, and settled fish and parrotfish are competitive. The innovation of the model is that, for the first time, the role of settled fish is taken into account in coral reef ecosystems, and a large number of experimental data show that settled fish play a vital role in maintaining the diversity of algae. So our model is better able to reflect the actual situation of coral reef ecosystems, and then we look at the dynamic behavior of the model (positive invariance, boundedness, The stability of fixed point and its bifurcation are studied in detail, and the numerical simulation of the system with given parameters is carried out. The third model continues to discuss the relationship between algae, settled fish and parrotfish. The difference is that we use the collaboration model proposed by May in 1976 to reflect the collaboration between algae and settled fish. The dynamic behavior of the system is studied in detail and numerically simulated. The mathematical tools used in this paper include Hartman-Grobman theorem, Routh-Hurwitz theorem and Sotomayor fixed point bifurcation theorem.
【學(xué)位授予單位】：上海師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

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本文編號(hào)：2455985