随机种群模型的散逸性

发布时间：2018-05-06 14:36

本文选题：随机种群模型 + 时变种群模型　；参考：《宁夏大学》2017年硕士论文

【摘要】：随机微分方程在经济、生物、生态等领域有广泛的应用.在现实生活中,因为存在着各种随机因素的影响,因此在随机微分方程上加上扰动就容易反映问题.比如在现实生活中的种群模型,其中的一些参数死亡率,出生率都是通过科学的统计方法估计出来的,然而在统计中研究种群问题都是在给定的置信度下,通过数据计算得出置信区间,因此我们的种群密度也是在一个区间上的,所以种群的密度也是不确定的.因此,一般的随机随机微分方程很难描述清楚这一类问题,为了清晰的说明问题,我们在随机微分方程中加入了模糊,Markov跳以及环境噪声等一些扰动因素.但是当种群模型中加入这些因素后,研究它们数值解很难,这里主要研究加入这些因素后,模型的散逸性.本文主要讨论了在随机微分方程背景下的与年龄相关的随机种群系统的散逸性行为.主要内容如下:(1)我们讨论了与年龄相关的模糊随机种群模型.在有界的条件(弱于线性增长条件)和Lipschitz条件下,利用It(?)公式和Bellman-Gronwall-Type引理,建立了与年龄相关的模糊随机种群扩散系统均方散逸性的判定准则,最后通过一些数值算例进行验证.(2)我们讨论了带Markov跳时变随机种群收获系统的数值解问题.利用Euler-Maruyama方法给出系统的解析解,在局部Lipschitz条件下,证明了方程的数值解在均方意义下收敛于其解析解.最后,通过数值例子对所给出的结论进行了验证.(3)我们讨论了一类在环境污染下与年龄相关的模糊随机种群系统,该模型考虑了环境污染、外界环境噪声对种群的影响,而且设初值是一个模糊数.在有界和Lipschitz条件下,运用Ito公式和Gronwall引理,给出了环境污染下与年龄相关模糊随机种群系统的均方散逸性.
[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.
【学位授予单位】：宁夏大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.63

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