| 一类带有自由边界的时间周期捕食—食饵模型 |
| Alternative Title | A class of the prey-predator model with a free boundary in time-periodic environment
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| 赵孟 |
| Thesis Advisor | 李万同
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| 2016-05-18
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| Degree Grantor | 兰州大学
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| Place of Conferral | 兰州
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| Degree Name | 硕士
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| Keyword | 捕食—食饵
时间周期
自由边界
扩张与灭绝
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| Abstract | 自然界中，由于日夜交替以及季节变化，许多生态现象都呈现出一定的时间周期性，因此考虑时间周期现象具有强烈的理论和现实意义。如果环境对种群生存与繁衍十分不利，那么种群往往会出现负增长现象，所以考虑内禀增长率变号同样重要。而且，生物入侵过程中，其种群的边界往往是变化的，这促使了自由边界问题的引入。因此，相对于固定区域上的周期问题，研究空间非齐次环境中的一类带有自由边界的时间周期捕食—食饵模型更能接近现实。
本文研究一类带有自由边界的时间周期捕食—食饵模型，其中，食饵在整个区域活动，而捕食者最初分散于一个小区域，此区域的边界随时间是动态变化的，且内禀增长率关于时间是周期变化的。首先，我们得到解的全局存在唯一性，然后证明扩张—灭绝二分性。同时，给出由捕食者的初始区域、扩散率、扩张能力和种群初始密度作为变量的扩张—灭绝二分性判据，最后，当扩张发生时，对扩张前沿的渐近扩张速度进行粗略估计。
结果表明，如果捕食者具有较大初始生活环境，那么捕食者会成功扩张，如果初始生活环境较小，则该种群要想成功扩张需有足够的扩张能力或者较高的初始密度。在防治害虫方面，引进其自然天敌是最环保的一种措施，本文的相关结果对此具有一定的指导意义。 |
| Other Abstract | In the nature world, the environment changes with the seasons, so some ecological phenomena change with time periodically. Hence, considering the time-periodic phenomenon has a strong theoretical and practical significance. When the environment is bad for the species' survival and reproduction, their intrinsic growth rate will be negative. So it is also important to consider that the intrinsic growth rate changes sign. In the process of biological invasion, the species' boundary varies with the time. This motivates previous researchers to introduce the free boundary problem. Hence, studying a class of the prey-predator model with a free boundary and sign-changing coefficient in time-periodic environment is more realistic than the corresponding periodic problem on the fixed region.
We consider the prey-predator model with sign-changing periodic intrinsic growth rate in heterogeneous time-periodic environment, where the prey species lives in the whole space but the predator species lives in a small region enclosed by a changeable boundary. Firstly, we get the global existence and uniqueness of the solutions. Then, we prove a spreading and vanishing dichotomy. Sharp criteria for spreading and vanishing with h_{0}, d_{1}, mu and u_{0}(x) as variable factors are obtained, where h_{0}, d_{1}, \mu and u_{0}(x) are the initial habitat size, the dispersal rate, expansion capacity and initial population size of the predator species, respectively. Moreover, some rough estimates of the asymptotic spreading speed are also given when spreading occurs.
The results show that, if the initial region is large enough, the predators will spread successfully. If the initial region is small, only the one with strong expansion capacity or large initial function will successfully spread. In order to control some pest species, we always put one kind of their natural enemies. The results of this paper have guiding significance to pest control. |
| URL | 查看原文
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| Language | 中文
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| Document Type | 学位论文
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| Identifier | https://ir.lzu.edu.cn/handle/262010/224509
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| Collection | 数学与统计学院
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Recommended Citation
GB/T 7714 |
赵孟. 一类带有自由边界的时间周期捕食—食饵模型[D]. 兰州. 兰州大学,2016.
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