本文選題：捕食系統(tǒng) + Allee效應(yīng)��； 參考：《蘭州交通大學(xué)》2015年碩士論文

【摘要】：近年來,隨著生態(tài)環(huán)境的不斷變化,很多物種受到Allee效應(yīng)的影響。Allee效應(yīng)會(huì)影響種群系統(tǒng)的穩(wěn)定性,甚至導(dǎo)致某些種群滅亡。因此,為了生態(tài)系統(tǒng)的健康發(fā)展,我們應(yīng)該對(duì)Allee效應(yīng)進(jìn)行深入的研究,這樣既能維持生態(tài)平衡,又能使資源得到合理的開發(fā)與利用,從而促進(jìn)可持續(xù)發(fā)展。本文主要應(yīng)用常微分理論知識(shí)和最優(yōu)控制理論知識(shí),本著積極探索的態(tài)度,對(duì)具有Allee效應(yīng)的捕食模型進(jìn)行了以下幾方面的研究。第一,建立了具有Allee效應(yīng)的廣義Logistic模型：該章首先分析了u=0時(shí),系統(tǒng)正平衡點(diǎn)的存在性和穩(wěn)定性,接著擴(kuò)充到u≠0,即含Allee效應(yīng)的廣義Logistic模型,對(duì)其正平衡點(diǎn)的的穩(wěn)定性態(tài)進(jìn)行討論,并考慮了該模型的最大可承受產(chǎn)量和最優(yōu)控制問題。這樣,同時(shí)滿足了人類的需要和種群的發(fā)展,也為后續(xù)的研究作了準(zhǔn)備。第二,考慮到自然界中食餌與捕食者的競爭關(guān)系,建立了捕食系統(tǒng)受Allee效應(yīng)的模型：該章考慮捕食系統(tǒng)受Allee效應(yīng)影響時(shí)的變化,并對(duì)食餌和捕食者同時(shí)進(jìn)行了最優(yōu)捕獲,從而控制生態(tài)平衡。本部分主要利用微分方程的近似系統(tǒng)得到了正平衡點(diǎn)漸進(jìn)穩(wěn)定的充要條件,通過構(gòu)造Lyapunov函數(shù),對(duì)系統(tǒng)的全局穩(wěn)定性進(jìn)行了證明,進(jìn)一步探究了生態(tài)平衡點(diǎn)的存在性,又從實(shí)際情況出發(fā),對(duì)系統(tǒng)進(jìn)行了捕獲優(yōu)化策略,最后通過數(shù)值模擬更清楚,直觀地驗(yàn)證了Allee效應(yīng)對(duì)種群穩(wěn)定性的影響。第三,根據(jù)生態(tài)系統(tǒng)發(fā)展規(guī)律,對(duì)捕食者受Allee效應(yīng)影響的模型進(jìn)行了研究：該章中建立了捕食者受Allee效應(yīng)影響的模型,采用與上一章相似的方法與理論對(duì)系統(tǒng)五個(gè)平衡點(diǎn)的性態(tài)進(jìn)行了分析,得到了正平衡點(diǎn)漸進(jìn)穩(wěn)定的充分條件,并證明其全局漸進(jìn)穩(wěn)定性,然后建立了人們需要的經(jīng)濟(jì)模型,研究了生態(tài)平衡點(diǎn),最后為了資源合理的開發(fā)利用,對(duì)食餌進(jìn)行了最優(yōu)收獲。最后,對(duì)本論文的整體框架及其結(jié)論進(jìn)行了歸納和展望,為該論文后續(xù)的研究與補(bǔ)充奠定了基礎(chǔ)。
[Abstract]:In recent years, with the continuous changes of ecological environment, many species will be affected by the Allee effect. Allee effect will affect the stability of the population system, and even lead to the extinction of some species. Therefore, in order to develop the ecosystem healthily, we should deeply study the Allee effect, which can not only maintain the ecological balance, but also make the resources reasonable development and utilization, thus promote the sustainable development. Based on the knowledge of ordinary differential theory and optimal control theory, the predation model with Allee effect is studied in this paper. First, the generalized Logistic model with Allee effect is established. In this chapter, the existence and stability of the positive equilibrium point of the system with u = 0 are analyzed, and then the generalized Logistic model with Allee effect is extended to u 鈮，

本文編號(hào)：1941164