Competitive exclusion in a nonlocal reaction–diffusion–advection model of phytoplankton populations. (October 2021)

• Record Type: Journal Article
• Authors: Jiang, Danhua; Lam, King-Yeung; Lou, Yuan
• Is Part Of: Nonlinear analysis. Volume 61(2021)
• Publication Date: 2021-10
• Subjects: Phytoplankton -- Integral equation -- Reaction–diffusion -- Infinite-dimensional dynamical system -- Monotone dynamical system -- Competitive exclusion; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103350
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We continue our study on the global dynamics of a nonlocal reaction–diffusion–advection system modeling the population dynamics of two competing phytoplankton species in a eutrophic environment, where both populations depend solely on light for their metabolism. In our previous work, we proved that system (1.1) is a strongly monotone dynamical system with respect to a non-standard cone related to the cumulative distribution functions, and further determined the global dynamics when the species have either identical diffusion rate or identical advection rate. In this paper, we study the trade-off of diffusion and advection and their joint influence on the outcome of competition. Two critical curves for the local stability of two semi-trivial equilibria are analyzed, and some new competitive exclusion results are obtained. Our main tools, besides the theory of monotone dynamical system, include some new monotonicity results for the principal eigenvalues of elliptic operators in one-dimensional domains.