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    政大機構典藏 > 理學院 > 應用數學系 > 期刊論文 >  Item 140.119/80558


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    题名: Wave propagation in the predator-prey systems
    作者: 符聖珍
    Fu, Sheng-Chen;Tsai, Je-Chiang
    贡献者: 應數系
    关键词: predator–prey system;travelling wave;spreading speed;super/sub-solution
    日期: 2015-12
    上传时间: 2016-01-13 16:23:53 (UTC+8)
    摘要: In this paper, we study a class of predator–prey systems of reaction–diffusion type. Specifically, we are interested in the dynamical behaviour for the solution with the initial distribution where the prey species is at the level of the carrying capacity, and the density of the predator species has compact support, or exponentially small tails near $x=\\pm \\infty $ . Numerical evidence suggests that this will lead to the formation of a pair of diverging waves propagating outwards from the initial zone. Motivated by this phenomenon, we establish the existence of a family of travelling waves with the minimum speed. Unlike the previous studies, we do not use the shooting argument to show this. Instead, we apply an iteration process based on Berestycki et al 2005 (Arch. Rational Mech. Anal. 178 57–80) to construct a set of super/sub-solutions. Since the underlying system does not enjoy the comparison principle, such a set of super/sub-solutions is not based on travelling waves, and in fact the super/sub-solutions depend on each other. With the aid of the set of super/sub-solutions, we can construct the solution of the truncated problem on the finite interval, which, via the limiting argument, can in turn generate the wave solution. There are several advantages to this approach. First, it can remove the technical assumptions on the diffusivities of the species in the existing literature. Second, this approach is of PDE type, and hence it can shed some light on the spreading phenomenon indicated by numerical simulation. In fact, we can compute the spreading speed of the predator species for a class of biologically acceptable initial distributions. Third, this approach might be applied to the study of waves in non-cooperative systems (i.e. a system without a comparison principle).
    關聯: Nonlinearity, 28, 4389-4423.
    数据类型: article
    DOI 連結: http://dx.doi.org/10.1088/0951-7715/28/12/4389
    DOI: 10.1088/0951-7715/28/12/4389
    显示于类别:[應用數學系] 期刊論文

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