【摘要】：本論文主要研究了兩類具有脈沖控制效應(yīng)的生態(tài)系統(tǒng)動力學(xué)問題,并對相關(guān)問題進(jìn)行深入地研究。論文首先介紹了生態(tài)系統(tǒng)動力學(xué)問題的研究背景和研究現(xiàn)狀,提供了論文研究所需的基本概念以及重要引理等基本知識,它們是后續(xù)章節(jié)討論的基礎(chǔ)。其次,研究了一類具有脈沖控制效應(yīng)的擴(kuò)散生態(tài)系統(tǒng)動力學(xué)問題。.推導(dǎo)得到了該生態(tài)動力學(xué)系統(tǒng)解的一致有界性、種群的持久生存性與滅絕性的閾值條件,證明了半平凡周期解的存在性、唯一性和全局漸近穩(wěn)定性。同時對該生態(tài)系統(tǒng)進(jìn)行了相關(guān)動力學(xué)數(shù)值模擬,模擬結(jié)果驗證了理論推導(dǎo)定理的有效性與可行性,并進(jìn)一步揭示了脈沖控制效應(yīng)對生態(tài)系統(tǒng)動力學(xué)行為的影響機(jī)制。再次,研究了一類具有脈沖控制效應(yīng)與季節(jié)效應(yīng)的生態(tài)系統(tǒng)動力學(xué)問題。分析了該生態(tài)系統(tǒng)半平凡周期解的存在性、局部漸近穩(wěn)定性和全局漸近穩(wěn)定性,討論了該生態(tài)系統(tǒng)種群的滅絕性與持久生存性,建立了相關(guān)動力學(xué)性質(zhì)的判定準(zhǔn)則。研究結(jié)果為進(jìn)一步研究如何運用脈沖控制策略維持生態(tài)種群持久生存提供了一定的理論支撐。最后,對研究結(jié)果進(jìn)行了總結(jié)和展望。
[Abstract]:In this paper, two kinds of ecosystem dynamics problems with pulse control effect are studied, and the related problems are studied deeply. Firstly, the background and present situation of ecosystem dynamics are introduced, and the basic concepts and important Lemma are provided, which are the basis of the discussion in the following chapters. Secondly, a kind of diffusion ecosystem dynamics problem with pulse control effect is studied. The threshold conditions for the existence, uniqueness and global asymptotic stability of the semi-trivial periodic solution are obtained. The simulation results verify the validity and feasibility of the theoretical derivation theorem, and further reveal the mechanism of the impulse control effect on the ecosystem dynamics behavior. Thirdly, a class of ecosystem dynamics problems with pulse control and seasonal effects are studied. In this paper, the existence, local asymptotic stability and global asymptotic stability of the semi-trivial periodic solution of the ecosystem are analyzed. The extinction and persistence of the ecosystem population are discussed, and the criteria for determining the dynamic properties of the ecosystem are established. The results provide a theoretical support for further study on how to use impulse control strategy to maintain the sustainable survival of ecological population. Finally, the research results are summarized and prospected.
【學(xué)位授予單位】：溫州大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

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本文編號：2411517