本文選題：隨機(jī)種群模型 + 時(shí)變種群模型�。� 參考：《寧夏大學(xué)》2017年碩士論文

【摘要】：隨機(jī)微分方程在經(jīng)濟(jì)、生物、生態(tài)等領(lǐng)域有廣泛的應(yīng)用.在現(xiàn)實(shí)生活中,因?yàn)榇嬖谥鞣N隨機(jī)因素的影響,因此在隨機(jī)微分方程上加上擾動(dòng)就容易反映問(wèn)題.比如在現(xiàn)實(shí)生活中的種群模型,其中的一些參數(shù)死亡率,出生率都是通過(guò)科學(xué)的統(tǒng)計(jì)方法估計(jì)出來(lái)的,然而在統(tǒng)計(jì)中研究種群?jiǎn)栴}都是在給定的置信度下,通過(guò)數(shù)據(jù)計(jì)算得出置信區(qū)間,因此我們的種群密度也是在一個(gè)區(qū)間上的,所以種群的密度也是不確定的.因此,一般的隨機(jī)隨機(jī)微分方程很難描述清楚這一類問(wèn)題,為了清晰的說(shuō)明問(wèn)題,我們?cè)陔S機(jī)微分方程中加入了模糊,Markov跳以及環(huán)境噪聲等一些擾動(dòng)因素.但是當(dāng)種群模型中加入這些因素后,研究它們數(shù)值解很難,這里主要研究加入這些因素后,模型的散逸性.本文主要討論了在隨機(jī)微分方程背景下的與年齡相關(guān)的隨機(jī)種群系統(tǒng)的散逸性行為.主要內(nèi)容如下:(1)我們討論了與年齡相關(guān)的模糊隨機(jī)種群模型.在有界的條件(弱于線性增長(zhǎng)條件)和Lipschitz條件下,利用It(?)公式和Bellman-Gronwall-Type引理,建立了與年齡相關(guān)的模糊隨機(jī)種群擴(kuò)散系統(tǒng)均方散逸性的判定準(zhǔn)則,最后通過(guò)一些數(shù)值算例進(jìn)行驗(yàn)證.(2)我們討論了帶Markov跳時(shí)變隨機(jī)種群收獲系統(tǒng)的數(shù)值解問(wèn)題.利用Euler-Maruyama方法給出系統(tǒng)的解析解,在局部Lipschitz條件下,證明了方程的數(shù)值解在均方意義下收斂于其解析解.最后,通過(guò)數(shù)值例子對(duì)所給出的結(jié)論進(jìn)行了驗(yàn)證.(3)我們討論了一類在環(huán)境污染下與年齡相關(guān)的模糊隨機(jī)種群系統(tǒng),該模型考慮了環(huán)境污染、外界環(huán)境噪聲對(duì)種群的影響,而且設(shè)初值是一個(gè)模糊數(shù).在有界和Lipschitz條件下,運(yùn)用Ito公式和Gronwall引理,給出了環(huán)境污染下與年齡相關(guān)模糊隨機(jī)種群系統(tǒng)的均方散逸性.
[Abstract]:Stochastic differential equations are widely used in economy, biology and ecology. In real life, because of the influence of various random factors, it is easy to reflect the problem by adding perturbation to the stochastic differential equation. For example, in real life population models, some of these parameters, mortality and birth rate, are estimated by scientific statistical methods. However, in statistics, the study of population problems is based on a given degree of confidence. The confidence interval is calculated by the data, so our population density is also in an interval, so the population density is also uncertain. Therefore, it is difficult for a general stochastic differential equation to describe this kind of problem clearly. In order to explain the problem clearly, we add some disturbance factors such as fuzzy Markov jump and ambient noise to the stochastic differential equation. But when these factors are added into the population model, it is difficult to study their numerical solution. In this paper, we mainly discuss the escape behavior of Age-dependent stochastic population systems in the context of stochastic differential equations. The main contents are as follows: 1) We discuss a fuzzy stochastic population model related to age. Under the bounded condition (weaker than the linear growth condition) and the Lipschitz condition, we use the ITO condition. Based on the formula and Bellman-Gronwall-Type Lemma, a criterion for determining the mean square escape of a fuzzy stochastic population diffusion system is established. Finally, some numerical examples are given to verify the problem of numerical solution of the stochastic population harvesting system with Markov hopping. The analytical solution of the system is obtained by using the Euler-Maruyama method. Under the local Lipschitz condition, it is proved that the numerical solution of the equation converges to its analytic solution in the sense of mean square. Finally, a numerical example is given to verify the proposed conclusions.) We discuss a class of age-dependent fuzzy stochastic population systems under environmental pollution. The model takes into account the effects of environmental pollution and environmental noise on the population. And let the initial value be a fuzzy number. Under bounded and Lipschitz conditions, using Ito formula and Gronwall Lemma, the mean-square escape of age-dependent fuzzy stochastic population system under environmental pollution is given.
【學(xué)位授予單位】：寧夏大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O211.63

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