本文選題：隨機干擾　切入點：平均持續(xù)生存　出處：《集美大學》2017年碩士論文　論文類型：學位論文

【摘要】：在現實生態(tài)系統(tǒng)中,生物間的活動總伴隨著各種隨機干擾,為了更加全面地描述客觀實際,隨機生態(tài)模型的應用研究愈來愈重要.目前隨機生態(tài)模型在種群動力學,流行病學等領域得到了廣泛的發(fā)展與應用.本文主要分三部分研究如下三類隨機生態(tài)模型的動力學行為:第一部分研究了具有負面效應的隨機浮游動植物模型.通過構造比較系統(tǒng)證明了全局正解的存在唯一性、均值有界性.接著得到了系統(tǒng)滅絕的充分條件,研究了隨機系統(tǒng)在對應確定性系統(tǒng)正平衡點處的漸近行為.最后,用數值模驗證了理論結果的正確性.第二部分研究了具有食餌染病和修正Leslie-Gower項的隨機捕食食餌模型.對于確定性系統(tǒng),證明了正平衡點的局部漸近穩(wěn)定性;對于隨機系統(tǒng),首先用It?o公式和隨機理論證明了系統(tǒng)全局正解的存在唯一性,其次給出了系統(tǒng)滅絕和強平均持續(xù)生存的充分條件,接著證明了在一定的條件下,系統(tǒng)存在唯一的平穩(wěn)分布.最后用數值模擬驗證了理論結果的正確性.第三部分研究了周期脈沖投放病毒的隨機害蟲治理模型.先證明了系統(tǒng)解的均值有界性和害蟲滅絕周期解的全局吸引性,接著討論了系統(tǒng)的滅絕性并得到系統(tǒng)非平均持續(xù)生存的閾值.最后利用數值模擬驗證了計算結果的正確性并豐富了所得理論結果.
[Abstract]:In the reality of ecological system, the biological activities of the total accompanied by various disturbances, to a more comprehensive description of the objective reality, and application of stochastic ecological model more important. At present the random ecological models in population dynamics, epidemiology and other fields has been widely development and application. The dynamic behavior of this paper is divided into three parts as follows three stochastic ecological model: the first part of the study has a negative effect of the random plankton model. By constructing the comparison system to prove the existence and uniqueness of global positive solutions, mean boundedness. Then the sufficient condition of the system of extinction obtained, study the asymptotic behavior in the corresponding deterministic system at the positive equilibrium point of the stochastic system. Finally, the numerical model to verify the correctness of the theoretical results. The second part studies the stochastic predator-prey model with disease in the prey and modified Leslie-Gower items Type. For deterministic systems, local asymptotic stability of the positive equilibrium is proved; for stochastic systems, the first It? O equation and the stochastic theory to prove the existence and uniqueness of positive solutions of the whole system, then gives the sufficient condition for system extinction and strong persistence in the mean, then proves that under certain conditions, the stationary distribution only exists in the system. Finally the simulation verify the correctness of the theoretical results by numerical simulation. The third part studies the stochastic model of pest control on virus cycle pulse. First prove that the mean system global boundedness and pest extinction cycle solution of attraction, then discussed the extinction of the system and the non average persistence of the threshold system. Finally using numerical simulation to verify the correctness of the calculation results and enrich the theoretical results.

【學位授予單位】：集美大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175

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本文編號：1611322