本文選題：脈沖擴散 + 周期環(huán)境　； 參考：《重慶師范大學(xué)》2017年碩士論文

【摘要】：在生態(tài)環(huán)境中,種群的擴散和遷徙是一個很普遍的現(xiàn)象,且在實際生活中種群的數(shù)量變化會受到天氣、季節(jié)等因素的影響,因此考慮周期環(huán)境下具有脈沖效應(yīng)的種群模型更具有實際意義.另外,利用脈沖微分方程來描述種群動力學(xué)的脈沖效應(yīng),如害蟲治理、捕撈、免疫等成為研究熱點.基于此,本文分別考慮在脈沖控制下的單斑塊和多斑塊的周期系數(shù)種群模型,給出害蟲滅絕周期解的穩(wěn)定性與持久性條件.全文主要分為兩個部分:第一部分主要考慮在不同脈沖時刻收割莊稼、噴灑農(nóng)藥以及釋放天敵等因素,研究具有周期系數(shù)的脈沖種群控制模型.利用脈沖微分方程比較原理、線性化方法以及Floquet原理,得到系統(tǒng)的害蟲滅絕周期解的局部漸近穩(wěn)定性和全局漸近穩(wěn)定性的充分條件.第二部分研究在斑塊環(huán)境下具有周期系數(shù)的植物害蟲天敵脈沖控制模型.在第一部分模型的基礎(chǔ)上,考慮種群的擴散性,將單斑塊模型推廣到m-斑塊模型,同時考慮在不同脈沖時刻進(jìn)行收割莊稼、噴灑農(nóng)藥以及釋放天敵.利用脈沖微分方程比較原理、線性化方法以及Floquet原理,我們得到系統(tǒng)害蟲滅絕周期解全局漸近穩(wěn)定性的充分條件.然后通過持久性理論得到該系統(tǒng)的持久性條件.最后給出2個斑塊情況下的數(shù)值例子,從而驗證所得結(jié)論.
[Abstract]:In the ecological environment, population diffusion and migration is a very common phenomenon, and in real life, the number of population changes will be affected by weather, season and other factors, Therefore, it is more meaningful to consider the population model with pulse effect in periodic environment. In addition, impulsive differential equations are used to describe the impulsive effects of population dynamics, such as pest control, fishing, immunity and so on. Based on this, the periodic coefficient population models of single and multiple patches under impulsive control are considered, respectively, and the stability and persistence conditions of the periodic solutions of pest extinction are given. The paper is divided into two parts: in the first part, the pulse population control model with periodic coefficient is studied by considering the factors of harvesting crops at different pulse times, spraying pesticides and releasing natural enemies. By using the comparison principle of impulsive differential equations, linearization method and Floquet principle, sufficient conditions for the local asymptotic stability and global asymptotic stability of the periodic solution of pest extinction are obtained. In the second part, the pulse control model of natural enemies of plant pests with periodic coefficient in patch environment is studied. Based on the first part of the model, considering the diffusion of population, the single patch model is extended to m- patch model. At the same time, harvesting crops, spraying pesticides and releasing natural enemies at different pulse times are considered. By using the comparison principle of impulsive differential equations, linearization method and Floquet principle, we obtain sufficient conditions for the global asymptotic stability of the periodic solution of pest extinction. Then the persistence condition of the system is obtained by persistence theory. Finally, numerical examples of two patches are given to verify the results.
【學(xué)位授予單位】：重慶師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

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