1. On a Competition-Diffusion-Advection System from River Ecology: Mathematical Analysis and Numerical Study.
- Author
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Xiao Yan, Hua Nie, and Peng Zhou
- Subjects
RIVER ecology ,MATHEMATICAL analysis ,NUMERICAL analysis ,WATERSHEDS ,REACTION-diffusion equations ,EIGENVALUES - Abstract
This paper is mainly concerned with a two-species competition model in open advective environments, where individuals cannot pass through the upstream boundary and do not return to the habitat after leaving the downstream boundary. By the theory of principal eigenvalue, we first obtain two critical curves (Γ
1 and Γ2 ) in the plane of bifurcation parameters that sharply determine the local stability of the two semitrivial steady states. Then under various conditions on given parameters, we discuss the global dynamics via different techniques, including the comparison principle for eigenvalues and perturbation and compactness arguments, and show that both competitive exclusion and coexistence are possible. For general values of parameters, we take both analytic and numerical approaches to further understand the potential behaviors of Γ1 and Γ2 , and we numerically observe that in addition to the competitive exclusion and coexistence, the bistable phenomenon is also possible, which is different from the known results of competitive ODE and reaction-diffusion systems (where bistability is impossible). The implication of our numerical results on future work is also discussed. [ABSTRACT FROM AUTHOR]- Published
- 2022
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