摘要(英) |
In this thesis, we first consider a Lotka-Volterra competition-diffusion-advection model for two competing species in a heterogeneous environment. The two species are identical except for their dispersal strategies: One is just random diffusion while the other is "smarter"- a combination of random diffusion and a directed movement up the environmental gradient. In [3], Chen and Lou conjectured that if the environment function $m$ has multiple local maxima, then the "smarter" species must concentrate at all local maximum of m. Nevertheless, in [6], Lam and Ni found that the "smarter" species will die out if the local maximum of m is smaller than the density of the other species. In this article, we consider a model of three species and expect that the related results will be similar to those in [6].
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參考文獻 |
[1] Fethi Belgacem and Chris Cosner, The effects of dispersal along environmental gradients on the dynamics of populations in heterogeneous environment, Canadian Appl. Math. Quart., 3 (1995), 379-397.
[2] Robert R. Cantrell, Chris Cosner and Yuan Lou, Advection mediation coexistence of competing species, Proc. Royal Soc. Edinburgh (A), 137 (2007), 497-518.
[3] Xinfu Chen and Yuan Lou, Principal eigenvalue and eigenfunction of elliptic operator with large convection and its application to a competition model, Indiana Univ. Math. J., 59 (2008), 627-658.
[4] Jack Dockery, Vivian Hutson, Konstantin Mischaikow and Mark Pernarowski, The evolution of slow dispersal rates: A reaction-diffusion model, J. Math. Biol., 37 (1998), 61-83.
[5] King-Yeung Lam, Concentration phenomena of a semilinear elliptic equation with large advection in population dynamics, J. Differential Equations, 250 (2011), 161-181.
[6] King-Yeung Lam and Wei-Ming Ni, Limiting profiles of semilinear elliptic equations with large advection in population dynamics, Dis. Cont. Dyn. Syst., 28 (2010), no. 3, 1051-1067.
[7] Vivian Hutson, Yuan Lou, and Konstantin Mischaikow, Convergence in competition models with small diffusion coefficients, J. Differential Equations, 211 (2005), no. 1, 135-161.
[8] Wei-Ming Ni, Diffusion and directed movement in heterogeneous environment, KAIST Mathematics colloquium, February 2011, Korea, downloaded from ”http://www.mathnet.or.kr/real/2011/02/WeiMingNi4(0224).pdf”.
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