Traveling waves for a reaction–diffusion–advection predator–prey model. (August 2017)

• Record Type: Journal Article
• Authors: Zhang, Tianran; Jin, Yu
• Is Part Of: Nonlinear analysis. Volume 36(2017)
• Page Start: 203
• Page End: 232
• Publication Date: 2017-08
• Subjects: 35K10 -- 92B05; Traveling waves -- Reaction–diffusion–advection equations -- Invasions -- Schauder's fixed-point theorem -- LaSalle's invariance principle -- Linear and nonlinear determinacy; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.01.011
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we study a reaction–diffusion–advection predator–prey model in a river. The existence of predator-invasion traveling wave solutions and prey-spread traveling wave solutions in the upstream and downstream directions is established and the corresponding minimal wave speeds are obtained. While some crucial improvements in theoretical methods have been established, the proofs of the existence and nonexistence of such traveling waves are based on Schauder's fixed-point theorem, LaSalle's invariance principle and Laplace transform. Based on theoretical results, we investigate the effect of the hydrological and biological factors on minimal wave speeds and hence on the spread of the prey and the invasion of the predator in the river. The linear determinacy of the predator–prey Lotka–Volterra system is compared with nonlinear determinacy of the competitive Lotka–Volterra system to investigate the mechanics of linear and nonlinear determinacy.