兰州大学机构库 >数学与统计学院
具有时滞的周期非均匀恒化器模型的空间动力学
Alternative TitleSpatial Dynamics of a Periodic Unstirred Chemostat Model with Delay
王雅
Thesis Advisor王智诚
2016-05-18
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword恒化器模型 存在唯一性 一致持久性 周期解 竞争排斥原理 共存
Abstract恒化器是一种基本的实验装置, 在生态学中具有重要作用. 它是具有恒定容积的微生物连续培养装置, 该装置通过输入营养液, 以及排出剩余营养液和有机物的混合物, 从而保持平衡. 通常情况下, 微生物摄取营养物后, 在将营养物转化为自身的生物量时存在时间滞后. 此外, 在微生物的连续培养过程中, 对营养基的输入一般是周期的. 因此, 研究具有时滞的非均匀搅拌的周期恒化器模型具有重要的意义. 本文主要研究一类具有时滞的非均匀周期恒化器模型的空间动力学. 主要内容如下: 首先, 通过考虑微生物的生物量的转化时间的滞后、营养液的周期输入以及非均匀搅拌等因素, 导出有界区域上的周期时滞反应扩散模型.其次, 研究单种营养基——单种微生物的恒化器模型. 利用动力系统理论和半 群理论研究该模型, 通过验证拟正条件, 给出了系统的解的全局存在唯一性, 并利用 链传递集理论给出了系统的一致持久性的充分条件. 最后, 研究单种营养基——双种微生物的竞争恒化器模型. 通过分析相应的线 性方程的 Poincaré 映射的谱半径, 建立了该模型的竞争排斥原理. 进一步, 给出了 两竞争物种共存的充分条件
Other AbstractThe chemostat is a basic piece of laboratory apparatus and it played an important role in ecology. It is a continuous culture device of constant volume for microorganisms into which a nutrient medium is pumped, balanced by an outflow that removes nutrients and organisms. Generally, for the microorganism, the delay is often caused by the conversion of consumed nutrient into itself. In addition, the nutrient concentration in the medium is maintained at the periodically varying concentration at the up stream end of the channel. Therefore, it is of importance to study the periodic unstirred chemostat model with delay. This thesis is devoted to spatial dynamics of a periodic and delayed reaction-advection-diffusion chemostat model. The main contents are as follows. Firstly, taking the periodicity, diffusion and delay into consideration, we derive a delayed reaction-advection-diffusion system with periodic boundary condition. Secondly, we study the single resource —— the single population model. By using the theory of dynamical system and semigroup, we investigate the current model system. Through verifying the quasi-positive condition, the existence and uniqueness of the global solution of the system is shown. Moreover, we present the sufficient conditions of the uniform persistence of the system. Finally, we study the single resource —— two competing populations model. By virtue of the analysis of the spectral radius of the Poincaré map of the associ- ated linear delayed reaction-advection-diffusion equation, we show the competitive exclusion principle for the model system. Furthermore, the sufficient conditions of the coexistence of two competing population are established.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224959
Collection数学与统计学院
Recommended Citation
GB/T 7714
王雅. 具有时滞的周期非均匀恒化器模型的空间动力学[D]. 兰州. 兰州大学,2016.
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