Dynamics of Lotka-Volterra diffusion-advection competition system with heterogeneity vs homogeneity
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Authors
Benlong Xu
- Department of Mathematics, Shanghai Normal University, Shanghai, 200234, P. R. China.
Hongyan Jiang
- Department of Mathematics, Shanghai Normal University, Shanghai, 200234, P. R. China.
Abstract
This paper mainly studies the dynamics of a Lotka-Volterra reaction-diffusion-advection model for two competing species which disperse by both random diffusion and advection along environmental gradient. In this model, the species are assumed to be identical except spatial variation: one lives in the heterogeneity environment, the other lives in the homogeneity environment. The main results of this paper are two fold: (i) The species living in homogeneous environment can never wipe out their competitor; (ii) Explore the condition on the diffusion and advection rates for exclusion and coexistence.
It is proved that for fixed dispersal rates, when the strength of the advection is sufficiently strong, the two competitive species coexist. This is a remarkable different result with that obtained by He and Ni recently for
corresponding systems without advection [X. He, W.-M. Ni, J. Differential Equations, \({\bf254}\) (2013), 528--546].
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ISRP Style
Benlong Xu, Hongyan Jiang, Dynamics of Lotka-Volterra diffusion-advection competition system with heterogeneity vs homogeneity, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 11, 6132--6140
AMA Style
Xu Benlong, Jiang Hongyan, Dynamics of Lotka-Volterra diffusion-advection competition system with heterogeneity vs homogeneity. J. Nonlinear Sci. Appl. (2017); 10(11):6132--6140
Chicago/Turabian Style
Xu, Benlong, Jiang, Hongyan. "Dynamics of Lotka-Volterra diffusion-advection competition system with heterogeneity vs homogeneity." Journal of Nonlinear Sciences and Applications, 10, no. 11 (2017): 6132--6140
Keywords
- Advection
- linear stability
- global asymptotic stability
- spatial heterogeneity
- coexistence
MSC
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