兰州大学机构库 >数学与统计学院
周期弱竞争Lotka-Volterra系统的行波解和渐近传播
Alternative TitleTraveling wave solutions and asymptotic spreading for a time periodic Lotka-Volterra system with weak competition
薄伟健
Thesis Advisor林国
2016-05-19
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword周期行波解 交错迭代 渐近传播速度 辅助系统 上下解
Abstract自然界中不同物种之间的竞争是不可避免的,因此有很多学者致力于研究不同竞争系统的动力学行为。 当然自然环境中很多因素都是随时间不断变化的,所以对周期竞争系统的研究也得到广泛关注。由于种群共存在实际情形中有着重要意义, 因此这里将从周期弱竞争 Lotka-Volterra系统出发,研究与共存平衡态有关的行波解以及渐近传播速度。 首先研究了周期行波解的存在性以及不存在性。 主要利用交错迭代方法并结合上下解方法证明系统周期行波解的存在性,并利用渐近传播理论以及单个方程的相关结论得出存在非平凡的周期行波解。之后运用渐近传播理论得出周期行波解的不存在性。这些结论表明了两个竞争种群在周期介质下可以成功共同入侵,并最终达到共存。 其次考虑了渐近传播速度。利用辅助系统并结合上下解方法,得出在周期介质下两个不同竞争种群的渐近传播速度。 结果表明种间竞争可以减慢某个种群的传播速度,从这个种群传播速度的上界可以看出非线性项对渐近传播速度的非平凡作用。
Other AbstractSince the interspecies competitive behavior can not be avoided, much attention has been paid to the dynamics behavior of different competition systems to describe the phenomena. Furthermore, there are many factors varying in time in the natural environment, then a time periodic competition system is arisen. One important topic is its traveling wave solutions. Due to the importance of coexistence state in ecology, in this thesis, we will study the travelling wave solutions as well as asymptotic spread relating the coexistence state of a time periodic Lotka-Volterra competition system with weak competition. Firstly, we investigate the existence and nonexistence of traveling wave solutions for the system. The existence of periodic traveling wave solutions is proved by using cross iteration and sub- and super-solutions methods. Moreover, by combining classical theory of asymptotic spread with the conclusion of a scalar equation, the existence of nontrivial time periodic traveling wave solutions is established. Then we obtain the nonexistence of time periodic traveling wave solutions by using the theory of asymptotic spread. These results illustrate that the co-invasions of two competitors are successful in periodic environment, and they can eventually attain to a coexistence state. Secondly, we consider the asymptotic speeds of spread. By combining auxiliary systems with sub- and super-solutions methods, we deduce some results about the asymptotic speeds of spread of the periodic system. The results indicate that the interspecific competition can decrease the invasion speed of one species, which implies that the nontrivial effect of nonlinear term for the invasion speed from up bound of the invasion speed.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224342
Collection数学与统计学院
Recommended Citation
GB/T 7714
薄伟健. 周期弱竞争Lotka-Volterra系统的行波解和渐近传播[D]. 兰州. 兰州大学,2016.
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