本文選題：數(shù)學(xué)模型 + 脈沖微分系統(tǒng)�。� 參考：《大連理工大學(xué)》2016年博士論文

【摘要】：眾所周知,在農(nóng)業(yè)生產(chǎn)中,生物種群的管理通常是根據(jù)人類(lèi)發(fā)展以及生態(tài)平衡等方面的因素來(lái)控制某一或某些種群的數(shù)量。對(duì)于一個(gè)生態(tài)系統(tǒng)中的害蟲(chóng),人們?cè)絹?lái)越意識(shí)到只有害蟲(chóng)種群數(shù)量達(dá)到經(jīng)濟(jì)閾值時(shí)進(jìn)行控制才是合理的做法。如何使重要的植物、動(dòng)物被害蟲(chóng)帶來(lái)的損失最小一直是人們所關(guān)心的問(wèn)題。本文以脈沖微分動(dòng)力系統(tǒng)為基礎(chǔ),考慮到殺蟲(chóng)劑所造成的蟲(chóng)害頻繁突發(fā)、環(huán)境污染及資源浪費(fèi)等問(wèn)題,分別從單種群害蟲(chóng)階段結(jié)構(gòu)模型、多種群害蟲(chóng).天敵模型及殺蟲(chóng)劑劑量反應(yīng)和害蟲(chóng)耐藥性發(fā)展的害蟲(chóng)-天敵模型的不同角度出發(fā),逐步給出了研究害蟲(chóng)控制的相應(yīng)策略。第二章考慮了一個(gè)狀態(tài)依賴脈沖的單種群階段結(jié)構(gòu)害蟲(chóng)治理模型,通過(guò)對(duì)成蟲(chóng)和幼蟲(chóng)總量的監(jiān)控,當(dāng)害蟲(chóng)達(dá)到經(jīng)濟(jì)閾值時(shí),采取化學(xué)控制。對(duì)半連續(xù)半動(dòng)力系統(tǒng),利用后繼函數(shù)方法,得到了系統(tǒng)階一周期解的存在性及吸引性的充分條件。通過(guò)數(shù)值模擬對(duì)有關(guān)結(jié)果進(jìn)行了驗(yàn)證。第三章基于害蟲(chóng)綜合控制策略(簡(jiǎn)稱IPM),建立了一個(gè)害蟲(chóng)綜合治理模型。分別討論了固定時(shí)刻不同頻率實(shí)施化學(xué)和生物控制的害蟲(chóng)控制策略以及固定時(shí)刻結(jié)合狀態(tài)依賴的混合控制的害蟲(chóng)控制策略對(duì)系統(tǒng)演化的影響。對(duì)于固定時(shí)刻不同頻率的噴灑殺蟲(chóng)劑及釋放天敵的控制策略,通過(guò)兩種不同策略給出了害蟲(chóng)滅絕周期解全局漸近穩(wěn)定及害蟲(chóng)天敵持續(xù)生存的充分條件。從數(shù)值上分析了臨界條件中噴灑殺蟲(chóng)劑次數(shù)和周期,投放天敵的數(shù)量,以及害蟲(chóng)和天敵的殘存率等對(duì)害蟲(chóng)的爆發(fā)和滅絕的影響,給出了害蟲(chóng)控制的合理噴灑殺蟲(chóng)劑次數(shù)及控制周期。對(duì)于混合控制的害蟲(chóng)綜合控制策略,從數(shù)值上分析了天敵對(duì)害蟲(chóng)爆發(fā)的影響。通過(guò)給出混合控制系統(tǒng)的平均爆發(fā)周期與系統(tǒng)中參數(shù)的關(guān)系,得到了主要影響害蟲(chóng)爆發(fā)周期的關(guān)健參數(shù)。第四章考慮到殺蟲(chóng)劑在進(jìn)入害蟲(chóng)體內(nèi)產(chǎn)生的滯后、殘留期以及常時(shí)間使用同一種殺蟲(chóng)劑可能產(chǎn)生對(duì)害蟲(chóng)的耐藥性等因素,通過(guò)殺蟲(chóng)劑劑量反應(yīng)函數(shù),建立了相應(yīng)的害蟲(chóng)綜合治理模型。分別討論了天敵不存在及存在時(shí),以害蟲(chóng)滅絕為控制目的的化學(xué)控制策略。當(dāng)天敵存在時(shí),對(duì)如下兩種不同控制策略：(1)殺蟲(chóng)劑噴灑次數(shù)大于天敵投放次數(shù)；(2)天敵投放次數(shù)大于殺蟲(chóng)劑噴灑次數(shù),給出了相應(yīng)的害蟲(chóng)滅絕周期解存在性及周期解局部漸近穩(wěn)定性的充分條件。利用數(shù)值模擬,研究了影響害蟲(chóng)爆發(fā)或滅絕的主要因素。討論了在不同噴灑殺蟲(chóng)劑次數(shù)或投放天敵次數(shù)條件下,噴灑和投放周期、噴灑劑量及環(huán)境對(duì)毒素的吸收對(duì)害蟲(chóng)滅絕臨界條件的影響。對(duì)害蟲(chóng)的耐藥性發(fā)展,在只進(jìn)行化學(xué)控制的害蟲(chóng)治理模型中引入了耐藥性發(fā)展方程,得到了害蟲(chóng)滅絕臨界條件。通過(guò)更換殺蟲(chóng)劑來(lái)應(yīng)對(duì)害蟲(chóng)的耐藥性發(fā)展問(wèn)題,依據(jù)不同的判斷標(biāo)準(zhǔn)給出了三種不同的更換殺蟲(chóng)劑策略。在綜合實(shí)施化學(xué)控制和生物控制時(shí),研究了投放天敵對(duì)害蟲(chóng)控制的影響,最終達(dá)到減少殺蟲(chóng)劑噴灑次數(shù)及更換次數(shù)的目的。
[Abstract]:It is well known that in agricultural production, the management of the biological population is usually based on the factors of human development and ecological balance to control the number of certain or certain populations. For a pest in an ecosystem, it is becoming more and more aware that it is reasonable to control only the number of pest populations when the number of pests reaches the economic threshold. This paper, based on the impulse differential dynamic system, takes into account the frequent occurrence of insect pests, environmental pollution and waste of resources, including the structure model of the single population pest stage, the model of natural enemies and the killing of natural enemies, respectively. In the second chapter, a single population phase structure pest management model of a state dependent pulse is considered, and the monitoring of the total amount of adults and larvae is taken when the pest reaches the economic threshold. Chemical control. In the semi continuous semi dynamic system, the sufficient conditions for the existence and attraction of the periodic solution of the order of the system are obtained by using the succeeding function method. The results are verified by numerical simulation. The third chapter, based on the integrated pest control strategy (IPM), establishes a comprehensive pest management model. The effect of chemical and biological control strategy on chemical and biological control at all times and the effect of the hybrid control strategy on the evolution of the system on the fixed time combined state dependent hybrid control strategy. For the control strategy of spraying insecticides and releasing natural enemies at different frequencies at fixed time, the extinction cycle of the pest is given through two different strategies. The sufficient conditions for the asymptotic stability of the Bureau and the sustainable survival of the natural enemies of the pests were analyzed. The effects of the number of insecticide spraying and the number of natural enemies and the residual rate of the pests and natural enemies on the outbreak and extinction of the pests were numerically analyzed. The number of insecticide spraying and the control period of the pest control were given. The control strategy of integrated pest control is used to analyze the influence of natural enemies on the outbreak of pests. By giving the relationship between the average burst period of the hybrid control system and the parameters in the system, the Guan Jian parameter which mainly affects the period of the pest outbreak is obtained. The fourth chapter takes into account the lag, residual period and the residual period of the insecticide in the pest. The resistance of the same insecticide to the pest is often used, and the integrated pest management model is established through the dose response function of the insecticide. The chemical control strategy for the control of the pest extinction when the natural enemy does not exist and exists is discussed respectively. When the natural enemy exists, the following two different control strategies are made. (1) the number of insecticide spraying is greater than the number of natural enemy release times; (2) the number of natural enemy release times is greater than the number of insecticide spraying. The sufficient conditions for the corresponding periodic solution and local asymptotic stability of the periodic solution are given. The main factors affecting the outbreak or extinction of the pests are studied by numerical simulation. The effects of spraying and releasing cycles, spraying dose and environment on the critical conditions of the pest were affected by the number of insecticides or the number of natural enemies, and the development of drug resistance was introduced in the chemical controlled pest control model, and the critical conditions for the extinction of the pests were obtained. In response to the resistance development of insect pests, three different kinds of insecticide replacement strategies were given according to the different criteria. In the comprehensive implementation of chemical control and biological control, the effects of natural enemies on pest control were studied. Finally, the purpose of reducing the number of spraying and changing times of insecticide was achieved.

【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：O175

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