本文選題：基于比率　切入點(diǎn)：捕食者-食餌系統(tǒng)　出處：《北方民族大學(xué)》2017年碩士論文

【摘要】：近年來,生物數(shù)學(xué)的迅速發(fā)展促進(jìn)了漁業(yè)、醫(yī)學(xué)、農(nóng)業(yè)、林業(yè)、生物信息學(xué)和細(xì)胞生物學(xué)等諸多領(lǐng)域的發(fā)展.而種群動力學(xué)則是生物數(shù)學(xué)中最經(jīng)典、最廣泛的研究領(lǐng)域之一.它為發(fā)展生物資源優(yōu)化管理和有害生物綜合治理等應(yīng)用領(lǐng)域奠定了堅(jiān)實(shí)的基礎(chǔ),為可再生資源的優(yōu)化管理提供了一定的理論指導(dǎo)意義.探究基于比率的三種群捕食者-食餌系統(tǒng)并分析其穩(wěn)定性對于保護(hù)種群資源具有深刻的實(shí)際意義.由于許多人為因素影響物種的捕獲,因此合理開發(fā)和保護(hù)種群資源顯得尤為重要.為此,本論文主要致力于種群動力學(xué)行為和更新資源優(yōu)化管理的研究,主要內(nèi)容有:(1)對基于比率的三種群捕食者-食餌模型進(jìn)行研究,運(yùn)用微分方程理論,RouthHurwitz判別法和Lyapunov穩(wěn)定性定理探討正平衡點(diǎn)的穩(wěn)定性并給出其充分條件.(2)利用微分方程穩(wěn)定性理論,Routh-Hurwitz判別法,Lyapunov穩(wěn)定性定理,Pontryagin最大值原理,探討了在雙密度制約的情形下,具有B-D功能反應(yīng)的捕食者-食餌系統(tǒng)的穩(wěn)定性和最優(yōu)捕獲策略,為生物種群的持久生存和開發(fā)管理提供了理論依據(jù)和指導(dǎo)意義.(3)研究了具有Michaelis-Menten功能反應(yīng)函數(shù)的捕食者-食餌系統(tǒng),根據(jù)微分方程穩(wěn)定性理論,Routh-Hurwitz判別法和Lyapunov穩(wěn)定性定理得到正平衡點(diǎn)存在及系統(tǒng)漸近穩(wěn)定的充分條件,最后采用Pontryagin最大值原理推導(dǎo)并獲得系統(tǒng)的最優(yōu)稅收策略.并利用MATLAB進(jìn)行數(shù)值模擬,檢驗(yàn)結(jié)果的正確性.
[Abstract]:In recent years, the rapid development of biological mathematics has promoted the development of fishery, medicine, agriculture, forestry, bioinformatics and cell biology.Population dynamics is one of the most classical and extensive research fields in biological mathematics.It lays a solid foundation for the development of optimal management of biological resources and integrated pest management and provides certain theoretical guidance for the optimal management of renewable resources.It is of great practical significance to explore the predator-prey system based on ratio and analyze its stability for the protection of population resources.Because many artificial factors affect species capture, it is very important to develop and protect population resources reasonably.Therefore, this thesis is mainly devoted to the research of population dynamics behavior and renewable resource optimization management. The main content of this paper is to study the predator-prey model of three species based on ratio.This paper discusses the stability of positive equilibrium point by using the theory of differential equation and Lyapunov stability theorem, and gives its sufficient condition. 2. Using the stability theory of differential equation, we use the theory of Routh-Hurwitz discriminant to discuss the Lyapunov stability theorem and the maximum value principle of Pontryagin.The stability and optimal capture strategy of a predator-prey system with B-D functional response under double density constraints are discussed.In this paper, the predator-prey system with Michaelis-Menten functional response function is studied, which provides a theoretical basis and guidance for the sustainable survival and development management of biological populations.According to the Routh-Hurwitz criterion and Lyapunov stability theorem of differential equations, sufficient conditions for the existence of positive equilibrium point and asymptotic stability of the system are obtained. Finally, the optimal tax policy of the system is derived and obtained by using the maximum Pontryagin principle.MATLAB is used to carry out numerical simulation to verify the correctness of the results.
【學(xué)位授予單位】：北方民族大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

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本文編號：1710081