具有白噪声干扰的随机扩散模型的研究

发布时间：2018-05-02 05:02

本文选题：灭绝性 + 持久性　；参考：《新疆大学》2015年硕士论文

【摘要】：种群的迁徙是自然界中最普遍的现象之一,研究种群的扩散对人类认识自然和生态系统具有重要的意义,许多生物数学学者对确定的种群扩散模型已经做了大量的研究,但对具有白噪声干扰的随机的种群扩散模型的研究却不多,因此在前人的研究基础上,我们也对几类具有白噪声干扰的扩散问题做了深入细致的研究,其中包括:一类具有白噪声干扰的单种群两斑块间的扩散;具有时滞的随机扩散系统和两斑块间具有对称扩散的随机捕食-食饵系统.本文的主要内容可以概述如下:1.第一节,介绍了本文研究的生物背景,然后介绍了有关随机模型的研究现状和一些研究成果.最后,介绍了本文的研究内容.2.第二节,提出了一类具有白噪声干扰的单种群两斑块间的扩散和具有时滞的随机扩散系统.通过构造合适的Liapunov函数,并且充分运用随机微分方程的伊藤公式和切比雪夫不等式得到了系统解的全局正性,有界性,持久性,灭绝性和平均积分有界.最后,通过数值模拟验证了理论结果.3.第三节,研究了两斑块间具有对称扩散的随机捕食-食饵系统.通过构造适当的Liapunov函数,运用伊藤公式和一些分析技巧,得到了捕食-食饵系统解的全局正性,有界性.利用随机微分方程的比较原理,伊藤公式及切比雪夫不等式,得到了系统的持久性及灭绝性.最后通过数值模拟验证了理论结果.4.第四节,对全文做了总结讨论.
[Abstract]:Population migration is one of the most common phenomena in nature. The study of population diffusion is of great significance to human understanding of nature and ecosystem. However, there are few researches on the random population diffusion model with white noise disturbance. Therefore, based on the previous studies, we have also done a thorough and detailed study on several kinds of diffusion problems with white noise interference. It includes a class of diffusion between two patches of a single population with white noise, a stochastic diffusion system with time delay and a stochastic predator-prey system with symmetric diffusion between two patches. The main contents of this article can be summarized as follows: 1. In the first section, the biological background of this paper is introduced, and then the research status and some achievements of stochastic models are introduced. Finally, this paper introduces the research content. 2. 2. In the second section, we propose a class of diffusion between two patches of a single population with white noise disturbance and a stochastic diffusion system with time delay. By constructing appropriate Liapunov functions and fully applying the Ito formula and Chebyshev inequality of stochastic differential equations, the global positivity, boundedness, permanence, extinction and mean integral boundedness of the solutions of the system are obtained. Finally, the theoretical results. 3. 3 are verified by numerical simulation. In the third section, the stochastic predator-prey system with symmetric diffusion between two patches is studied. By constructing proper Liapunov function, using Ito formula and some analytical techniques, the global positivity and boundedness of the solution of predator-prey system are obtained. By using the comparison principle of stochastic differential equation, Ito formula and Chebyshev inequality, the permanence and extinction of the system are obtained. Finally, the theoretical results are verified by numerical simulation. 4. The fourth section, has made the summary discussion to the full text.
【学位授予单位】：新疆大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O211.63

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