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题名 具有时滞的种内与种间竞争模型及其动态模拟
姓名 罗虎明
院系 数学与统计学院
专业 应用数学
学位名称 理学硕士
外文题名 the researches on the computer modeling experiment of intra-and inter-specific competition with time lags
第一导师姓名 李自珍
关键词 时滞;竞争;数学模型;种群动态;计算机模拟;离散;连续;稳定性
外文关键词 time lag;competition;mathematics model;population dynamics;computer modeling experiment;discrete;continuous;stability
学科 理学
摘要 种群动态是生态学研究的重要内容。影响种群波动的因素很多,时滞就是其 中之一。本文系统地探讨了种内与种间竞争的理论机制与过程,组建了具有时滞 的种内和种间竞争模型并进行计算机模拟分析,研究了时滞效应在单种群数量变 动以及数量变动周期中的影响作用和时滞效应在两竞争种群中的作用,进行了实 例分析。主要得到以下结论: 1.通过对具有时滞的离散和连续种内竞争模型的模拟研究发现,时滞是导致种 群不稳定的重要因素,一般时滞越长,种群越不稳定。时滞也是一把双刃剑,除 了导致系统的不稳定外,有时候对系统,也有稳定的作用。 2.通过对离散时滞模型: Nt+1 = [1:0 ¡ b(Nt¡T ¡ Neq)]Nt Nt+1 = rNt(1 ¡ Nt¡T K ) 的模拟研究,发现种群波动周期数等于:4T + 2(T是时滞)。同时,证明 了T = 1; 2时,结论是正确的。 3. 从具有时滞的种间竞争系统可见,时滞的影响还是很大的。随着时滞的增 大,种群数量逐渐出现大幅度的波动,还可能出现周期性的波动,系统逐渐变得 不稳定。从竞争系数都大于1的情况可以发现,时滞的增大也会使原来竞争系数大 的强种群,变为弱种群,被排斥出去。 4.以沙区两种主要固沙植物为对象,提出了改进的植物种间竞争模型,进行了 实例的计算与分析,揭示了种间竞争作用过程与共存机理。 以上结果,扩展了种内与种间竞争理论,建立了具有时滞效应的竞争新模 型,进行了数值分析,其实例分析结果对于沙区生态恢复具有应用前景。
外文摘要 Population dynamics is an important content in research on ecology. Factors that affect the fluctuating of populations are many, and time lag is one of them. This work systematically analyzed the theoretical mechanism and process of intra- and inter-specific competition. We established the intra- and inter-specific competition models with time lags and simulated it in computer; And we researched the role of time lag effects on onespecies population fluctuating and its period, and on two-species competitive population; We analyzed specific examples. We mainly obtain the following conclusions: 1), By simulating and studying the discrete and continuous intra-specific competition models with time lags, we find that: time lags are important factor that cause populations unstable. In general, the longer the time lags, the less stable the populations. 2), By simulating and researching the following discrete models with time lags, we find that: the number of the populations'''' fluctuating period equates to 4T+2 (T is time lag), at the same time, we proved that our conclusion of the above is correct at T=1, 2. Nt+1 = [1:0 ¡ b(Nt¡T ¡ Neq)]Nt Nt+1 = rNt(1 ¡ Nt¡T K ) 3), From the researching on intra-specific competition system with time lags, we can see that: the influence of time lags are very strong; With the increasing of time lags, large extent fluctuating will gradually arise for the number of populations; It is also possible that the periodical fluctuation of the system arise, therefore, the system will gradually become unstable. Seeing from the cases that the competition coefficients are all bigger than 1, we can know that, with the increasing of time lags, the strong population with big competition coefficients can also become weak population and fail to compete with its competitor. 4), By researching two dominating sand-fixation plants in sand area, we established improved intra-specific competition model of plants; We calculated and numerically analyzed the specific examples; We demonstrated the role and process of intra-specific competition, and the mechanism of coexistence. The above results expand the theory of intra- and inter-specific competition, and the analyzed results of specific examples have application perspective in ecological restoring.
研究领域 生物数学与系统优化
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