【摘要】：紅松是我國東北地區(qū)的重點保護(hù)樹種.紅松的物種價值不僅體現(xiàn)在保護(hù)生態(tài)環(huán)境方面,也體現(xiàn)在經(jīng)濟(jì)方面.因此,對于紅松生態(tài)系統(tǒng)的研究具有重要的意義.考慮到雌鼠的乳汁為剛出生的幼鼠提供了所有身體所需的營養(yǎng),這讓正在哺乳期的雌鼠將加大采集、捕食和埋藏松籽的力度,繼而使得松籽被埋藏于地表的概率增大,增加了松籽被遺漏的可能性,處在特別適宜松籽萌發(fā)成幼苗環(huán)境的被遺漏的松籽就萌發(fā).因此,要想讓對紅松種群的研究更切合實際情況把鼠類的哺乳期考慮在內(nèi)很有必要.本文考慮了鼠類的哺乳期這一實際現(xiàn)象,建立了四類線性和非線性的具有時滯的反映松籽、鼠類和幼苗三者之間相互關(guān)系的紅松種群數(shù)學(xué)模型.對本文的四類具有時滯的紅松種群模型,時滯微分方程的知識被用來對模型進(jìn)行研究,數(shù)值模擬了松籽、鼠類、幼苗及三者對時滯參數(shù)鼠類的哺乳期的走勢,得出時滯參數(shù)對三者呈現(xiàn)有規(guī)律的穩(wěn)定特性的影響.本文研究成果是天然紅松林系統(tǒng)的松籽、鼠類和幼苗三者之間在一定條件下可以形成一個隨時間變化互為消長并且有規(guī)律的周期性振蕩,并最終保持動態(tài)穩(wěn)定.全文包括五章內(nèi)容.緒論是第一章,主要闡述課題的研究背景及研究的目的和意義、紅松種群模型的國內(nèi)外研究現(xiàn)狀、主要內(nèi)容及本文所用到的基礎(chǔ)知識.第二章建立了一類線性時滯紅松種群的模型,這里的時滯參數(shù)是鼠類哺乳期,本章最先分析和判定了正平衡點的穩(wěn)定性,給出了時滯界限,導(dǎo)出存在Hopf分支的條件.第三章構(gòu)造了兩個非線性時滯紅松種群的模型,本章先分析和判定正平衡點的穩(wěn)定性,接著通過運用理論知識分析得Hopf分支方向和分支周期解的穩(wěn)定性的相關(guān)公式.第四章構(gòu)造了人工開發(fā)線性時滯紅松種群模型,本章最先分析和判定了正平衡點的穩(wěn)定性,獲得了發(fā)生Hopf分支條件及產(chǎn)生了分支周期解.第五章是本文的主要結(jié)論和展望.
[Abstract]:Pinus koraiensis (Pinus koraiensis) is a key protected tree species in northeast China. The species value of Pinus koraiensis is not only reflected in the protection of ecological environment, but also in the economic aspect. Therefore, it is of great significance for the study of Pinus koraiensis ecosystem. Considering that the milk of the female mice provides all the nutrients needed by the body for the newborn mice, which makes the lactating female rats more likely to gather, hunt and bury the pine seeds, which in turn increases the probability that the pine seeds are buried on the surface, The possibility of pine seeds being missed is increased, and the missed pine seeds germinate in a suitable environment for pine seeds to germinate into seedlings. Therefore, it is necessary to consider the lactation period of rodents in order to make the study of Pinus koraiensis population more realistic. In this paper, four kinds of linear and nonlinear mathematical models of Pinus koraiensis population, which reflect the relationship among pine seeds, rodents and seedlings, are established by taking into account the actual phenomenon of the lactation period of rodents, and four kinds of linear and nonlinear mathematical models of Korean pine population with time delay are established. The knowledge of delay differential equation is used to study the four types of Pinus koraiensis population models in this paper. The trends of lactation period of pine seeds, rodents, seedlings and three kinds of delay parameter rodents are numerically simulated. The effects of time-delay parameters on the stability of the three parameters are obtained. The results of this study are the pine seeds of the natural Korean pine forest system. Under certain conditions, the rodents and seedlings can form a periodic oscillation which fluctuates and fluctuates regularly with each other with time, and finally keeps the dynamic stability. The full text includes five chapters. The introduction is the first chapter, which mainly describes the research background, the purpose and significance of the research, the domestic and foreign research status of Pinus koraiensis population model, the main contents and the basic knowledge used in this paper. In the second chapter, the model of a class of linear delay Korean pine population is established, where the delay parameter is mouse lactation. In this chapter, the stability of positive equilibrium point is first analyzed and determined, the delay bound is given, and the conditions for the existence of Hopf bifurcation are derived. In chapter 3, two nonlinear delay Korean pine population models are constructed. In this chapter, the stability of positive equilibrium point is analyzed and determined, and then the stability formulas of Hopf bifurcation direction and bifurcation periodic solution are obtained by using theoretical knowledge. In chapter 4, we construct the artificial development linear delay Korean pine population model. In this chapter, we first analyze and determine the stability of the positive equilibrium point, obtain the Hopf bifurcation condition and produce the bifurcation periodic solution. The fifth chapter is the main conclusion and prospect of this paper.
【學(xué)位授予單位】：北京建筑大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 劉慶洪;落葉松人工林中紅松種群發(fā)生的初步研究[J];東北林業(yè)大學(xué)學(xué)報;1986年03期

2 葛劍平,郭海燕,陳動;小興安嶺天然紅松林種群結(jié)構(gòu)的研究[J];東北林業(yè)大學(xué)學(xué)報;1990年06期

3 李群宏,陸啟韶,雷錦志;紅松林種群模型的極限環(huán)[J];廣西大學(xué)學(xué)報(自然科學(xué)版);1999年04期

4 劉陽陽;宋國華;王曉靜;馬琳;;一類松籽、鼠類、幼樹的動態(tài)數(shù)學(xué)模型討論及模擬[J];北京建筑工程學(xué)院學(xué)報;2013年02期

5 劉慶洪;;小興安嶺紅松種群天然更新的特點[J];林業(yè)科學(xué);1987年03期

6 吳詠蓓,張恩迪;地理信息系統(tǒng)(GIS)在動物生態(tài)學(xué)中的應(yīng)用[J];生態(tài)科學(xué);2000年04期

7 李典謨,馬祖飛;展望數(shù)學(xué)生態(tài)學(xué)與生態(tài)模型的未來[J];生態(tài)學(xué)報;2000年06期

8 姬蘭柱,劉足根,郝占慶,王慶禮,王淼;松果采摘對長白山闊葉紅松林生態(tài)系統(tǒng)健康的影響[J];生態(tài)學(xué)雜志;2002年03期

9 宋國華;天然林內(nèi)紅松種群年齡更替數(shù)學(xué)模型及研究[J];生物數(shù)學(xué)學(xué)報;1994年04期

10 鄭祖庥;泛函微分方程的發(fā)展和應(yīng)用[J];數(shù)學(xué)進(jìn)展;1983年02期

相關(guān)博士學(xué)位論文 前2條

1 王曉靜;紅松種群數(shù)學(xué)模型及其動力學(xué)行為研究[D];北京林業(yè)大學(xué);2011年

2 顏向平;時滯Lotka-Volterra擴(kuò)散系統(tǒng)的分支與周期解[D];蘭州大學(xué);2007年

相關(guān)碩士學(xué)位論文 前2條

1 彭永立;泛函微分方程分支理論在生物數(shù)學(xué)的應(yīng)用[D];華東師范大學(xué);2009年

2 劉陽陽;天然紅松林種群生長的動力學(xué)行為研究[D];北京建筑大學(xué);2014年

，

本文編號：2465591