本文關(guān)鍵詞： Hopf分岔 雙時滯 率依賴 功能反應(yīng)函數(shù)　出處：《江蘇大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：生態(tài)系統(tǒng)具有復(fù)雜性和多樣性,對應(yīng)的種群生態(tài)系統(tǒng)模型具有著豐富動力學(xué)性質(zhì),因而探究種群生態(tài)系統(tǒng)理論中的奧秘已成為當(dāng)下的熱點(diǎn)研究課題之一。值得一提的是,由于諸如多時滯、率依賴等影響因素廣泛存在于種群生態(tài)系統(tǒng),因此考慮這些因素能夠更加貼切的描述自然生態(tài)系統(tǒng)的真實(shí)狀態(tài)�；诖吮尘�,本文重點(diǎn)討論了兩類含多時滯的捕食-食餌模型的動力學(xué)特征及其性質(zhì)。首先,本文對國內(nèi)外的研究現(xiàn)狀作了調(diào)查并進(jìn)行歸納整理,給出了選題的背景及意義。其次,重點(diǎn)探究了含率依賴、反饋和妊娠時滯的HollingIII功能反應(yīng)函數(shù)生態(tài)傳染病系統(tǒng)模型。在系統(tǒng)中將兩個時滯項(xiàng)看作分岔參數(shù),深入地討論了該模型正平衡點(diǎn)的穩(wěn)定性,并且應(yīng)用Hopf分岔理論,給出了平衡點(diǎn)處發(fā)生Hopf分岔的條件。運(yùn)用動力學(xué)理論得到了系統(tǒng)的分岔方向和相應(yīng)的周期解,最后模擬驗(yàn)證了本文的結(jié)論。接下來,研究了帶有階段結(jié)構(gòu)、功能反應(yīng)函數(shù)、選擇收獲時滯以及避難時滯的捕食-食餌系統(tǒng)模型。同樣地,結(jié)合穩(wěn)定性理論和分岔理論探究了該模型的分岔?xiàng)l件及周期解,與之前不考慮食餌避難因素的模型相比,此模型更具有避免食餌滅絕的現(xiàn)實(shí)意義,數(shù)據(jù)模擬驗(yàn)證理論分析的正確性。最后,系統(tǒng)的總結(jié)了論文的研究工作,同時指出了本文需要改進(jìn)之處,并對今后進(jìn)一步的研究目標(biāo)及方向作出展望。
[Abstract]:The ecosystem is complex and diverse, and the corresponding population ecosystem model has rich dynamic properties. Therefore, exploring the mystery of population ecosystem theory has become one of the hot research topics. It is worth mentioning that, because of such factors as multi-delay, rate-dependent and other factors widely exist in the population ecosystem. Therefore, considering these factors can more accurately describe the real state of the natural ecosystem. Based on this background, this paper focuses on the dynamic characteristics and properties of two kinds of predator-prey models with multiple delays. In this paper, the current research situation at home and abroad has been investigated and summarized, and the background and significance of the topic have been given. Secondly, the emphasis has been put on the research of percentage dependence. The HollingIII functional response function Eco-infectious system model with feedback and pregnancy delay is presented. The stability of the positive equilibrium point of the model is discussed in depth by considering the two time-delay terms as bifurcation parameters in the system. By using the Hopf bifurcation theory, the condition of Hopf bifurcation at the equilibrium point is given, and the bifurcation direction and the corresponding periodic solution are obtained by using the dynamics theory. Finally, the conclusion of this paper is verified by simulation. Then, the predator-prey system model with stage structure, functional response function, harvest delay and asylum delay is studied. Combined with the stability theory and bifurcation theory, the bifurcation conditions and periodic solutions of the model are explored. Compared with the previous model, which does not consider the factors of prey refuge, the model has more practical significance of avoiding prey extinction. Data simulation verifies the correctness of the theoretical analysis. Finally, the paper summarizes the research work, points out that this paper needs improvement, and makes a prospect for the future research goal and direction.
【學(xué)位授予單位】：江蘇大學(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

1 ;Stability and Hopf bifurcation of a delayed ratio-dependent predator-prey system[J];Acta Mechanica Sinica;2011年02期

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本文編號：1484684