两类随机种群生物动力系统的研究

发布时间：2018-05-02 23:24

本文选题：脉冲随机微分方程 + 随机持久性　；参考：《湖北民族学院》2015年硕士论文

【摘要】：在现实世界中,生态系统不可避免地要受到环境噪声的干扰,为了客观真实地揭示环境噪声对生态系统的影响,我们有必要建立并研究相应的随机生态数学模型.本文结合生物动力学模型和随机微分方程的相关理论知识,具体研究了两类随机生态数学模型的动力学行为,并给出了具体的例子及对应的数值模拟.全文共分为四章:第一章概述了随机生物数学模型的选题背景、研究意义和研究现状以及简单介绍本文所做的主要工作.第二章简要介绍了本文相关的概率论、随机过程、随机微积分及脉冲随机微分方程等基础知识和相关的定义、引理、符号说明.第三章研究了一类非自治的单种群脉冲随机微分方程模型.应用相关的预备知识和构造Lyapunov函数,证明了系统全局正解的存在唯一性,并在此基础上分析该系统的随机持久性、绝灭性、轨道渐近估计、全局吸引性等动力学行为.此外,我们给出了具体的例子及对应的数值模拟.第四章研究了一类自治的两种群竞争系统的随机微分方程模型.利用随机微分方程的比较定理、?Ito公式、矩不等式、Chebyshev不等式、Cp不等式以及构造Lyapunov函数的方法,讨论了该系统全局正解的存在唯一性、随机最终有界性,并研究了该系统的全局吸引性.此外,我们给出了具体例子及对应的数值模拟.
[Abstract]:In the real world, the ecosystem will inevitably be disturbed by the environmental noise. In order to reveal the effect of the environmental noise on the ecosystem objectively and realistically, it is necessary to establish and study the corresponding random ecological mathematical model. Based on the theoretical knowledge of biodynamic model and stochastic differential equation, this paper studies the dynamic behavior of two kinds of stochastic ecological mathematical models in detail, and gives concrete examples and corresponding numerical simulations. The thesis is divided into four chapters: the first chapter summarizes the background, research significance and research status of stochastic biological mathematical model, and briefly introduces the main work done in this paper. In chapter 2, we briefly introduce the basic knowledge of probability theory, stochastic process, stochastic calculus and impulsive stochastic differential equation, and their definitions, Lemma and symbolic explanation. In chapter 3, we study a class of nonautonomous impulsive stochastic differential equations with single population. The existence and uniqueness of the global positive solution of the system are proved by using the related preparatory knowledge and the construction of Lyapunov function. On this basis, the dynamical behaviors of the system such as stochastic persistence, extinction, asymptotic estimation of orbit and global attractiveness are analyzed. In addition, we give specific examples and corresponding numerical simulations. In chapter 4, the stochastic differential equation model of a class of autonomous two species competition system is studied. By using the comparison theorem of stochastic differential equation and Ito formula, the moment inequality and Chebyshev inequality and the method of constructing Lyapunov function, the existence and uniqueness of the global positive solution of the system are discussed, and the stochastic ultimate boundedness is discussed. The global attractiveness of the system is studied. In addition, we give specific examples and corresponding numerical simulations.
【学位授予单位】：湖北民族学院
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O211.63

【共引文献】