幾類具有功能反應(yīng)和收獲率的捕食者食餌系統(tǒng)的定性分析

1、 獨(dú)創(chuàng)性 獨(dú)創(chuàng)性(或創(chuàng)新性 或創(chuàng)新性)聲明 聲明 本人聲明所呈交的論文是我個(gè)人在導(dǎo)師指導(dǎo)下進(jìn)行的研究工作及取得的研究成果.盡我所知， 除了文中特別加以標(biāo)注和致謝中所羅列的內(nèi)容以外， 論文中不包含其他人已經(jīng)發(fā)表或撰寫過的研究成果； 也不包含為獲得桂林電子科技大學(xué)或其它教育機(jī)構(gòu)的學(xué)位或證書而使用過的材料. 與我一同工作的同志對本研究所做的任何貢獻(xiàn)均已在論文中做了明確的說明并表示了謝意. 申請學(xué)位論文與資料若有不實(shí)之處，本人承擔(dān)一切相關(guān)責(zé)任

2、. 本人簽名： 日期： 關(guān)于論文使用授權(quán)的說明 關(guān)于論文使用授權(quán)的說明 本人完全了解桂林電子科技大學(xué)有關(guān)保留和使用學(xué)位論文的規(guī)定， 即： 研究生在校攻讀學(xué)位期間論文工作的知識產(chǎn)權(quán)單位屬桂林電子科技大學(xué). 本人保證畢業(yè)離校后，發(fā)表論文或使用論文工作成果時(shí)署名單位仍然為桂林電子科技大學(xué).學(xué)校有權(quán)保留送交論文的復(fù)印件，允許查閱和借閱論文；學(xué)校可以公布論文的全部或部分內(nèi)容，可以允許采用影印、縮印或其它復(fù)制手段保存論文.(保密的論文在解密后

3、遵守此規(guī)定) 本學(xué)位論文屬于保密在____年解密后適用本授權(quán)書. 本人簽名： 日期： 導(dǎo)師簽名： 日期： Abstract Abstract A predator-prey model is the central content of population dynamics, Population dynamics behavior can be described in differential equations. In

4、a mathematical sense, population dynamics research can help mankind to development and control biological populations. The thesis mainly researches three classes of predator-prey with functional response and harvesting r

5、ates. Qualitative analysis is made by employing the qualitative theory of ordinary differential equations and the related theories of the delay differential equations, the sufficient condition for guaranteeing the perman

6、ence of the system and global asymptotic stability are established. The thesis consists of six chapters. The first part reviews the development history and significance of the mathematical biology and population ecology.

7、 The second part introduces the related theory on differential equations and population dynamics. In the third part, on the basis of a class of autonomous system with double density restrict, a nonautonomous system with

8、Bedding-DeAngelis functional responses, investing rates and harvesting rates is discussed. Sufficient conditions are obtained for permanence and global asymptotic stability of the system by using the analytical approach

9、and constructing a suitable Lyapunov function. In the fourth part, a predator-prey model with Allee effect and a constant prey refuge is considered. By using differential equations basic theory, the positive boundedness

10、of the solutions is proved. At the same time, the existence and stability of the positive equilibrium point are analyzed. Finally, some sufficient conditions for the existence and nonexistence limit cycles of the model a

11、re obtained. In the fifth part, a predator-prey system with HollingⅡ functional response and time-delays is investigated. By analyzing the corresponding characteristic and constructing a suitable Lyapunov functional, the

12、 existence of the equilibrium points is proved, and the sufficient conditions are derived for the global asymptotic stability of the positive equilibrium, the existence of Hopf bifurcation is also discussed. The sixth pa

13、rt summed up the research results and pointed out the inadequacy of the paper, and forecasts the future research tendency. Key words: predator-prey system; functional response; permanence; time-delay; global asymptotica