Positive steady states for a prey–predator model with population flux by attractive transition. (December 2018)

• Record Type: Journal Article
• Authors: Oeda, Kazuhiro; Kuto, Kousuke
• Is Part Of: Nonlinear analysis. Volume 44(2018)
• Page Start: 589
• Page End: 615
• Publication Date: 2018-12
• Subjects: Prey–predator model -- Attractive transitional flux -- Coexistence steady states -- A priori estimate -- Bifurcation analysis -- Asymptotic behavior; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.06.006
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper studies the stationary solutions of a prey–predator model with population flux by attractive transition. We first obtain a bifurcation branch (connected set) of positive solutions which connects two semitrivial solutions. Next we derive the asymptotic behavior of positive solutions as the coefficient α of the population flux tends to infinity. A main result implies that positive solutions can be classified into two types as α → ∞ . In one type of them, as α → ∞, positive solutions of the prey–predator model approach positive solutions of a competition model with equal diffusion coefficients.