Traveling waves for a periodic Lotka–Volterra predator–prey system. Issue 14 (26th October 2019)

• Record Type: Journal Article
• Authors: Wang, Xinjian; Lin, Guo
• Is Part Of: Applicable analysis. Volume 98:Issue 14(2019)
• Page Start: 2619
• Page End: 2638
• Publication Date: 2019-10-26
• Subjects: Minimal wave speed -- upper and lower solutions -- analytic semigroup -- asymptotic spreading; 35K57 -- 35B40 -- 92D40; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1469007
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: This paper is concerned with the time periodic traveling wave solutions for a periodic Lotka–Volterra predator–prey system, which formulates that both species synchronously invade a new habitat. We first establish the existence of periodic traveling wave solutions by combining the upper and lower solutions with contracting mapping principle and Schauder's fixed point theorem. The asymptotic behavior of nontrivial solution is given precisely by the stability of the corresponding kinetic system that has been widely investigated. Then, the nonexistence of periodic traveling wave solutions is confirmed by applying the theory of asymptotic spreading. We show the conclusion for all positive wave speed and obtain the minimal wave speed.