Existence and non-monotonicity of traveling wave solutions for general diffusive predator-prey models

Cheng Hsiung Hsu, Jian Jhong Lin

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

This paper is concerned with the existence and non-monotonicity of traveling wave solutions for general diffusive predator-prey models. By using Schauder’s fixed point theorem and the existence of contracting rectangles, we obtain the existence result. Then we investigate the asymptotic behavior of positive monotone traveling wave solutions by using the modified Ikehara’s Theorem. With the help of their asymptotic behavior, we provide a sufficient condition which guarantee that all positive traveling wave solutions of the system are non-monotone. Furthermore, to illustrate our main results, the existence and non-monotonicity of traveling wave solutions of Lotka-Volterra predator-prey model and modified Leslie-Gower predator-prey models with different kinds of functional responses are also discussed.

Original languageEnglish
Pages (from-to)1483-1508
Number of pages26
JournalCommunications on Pure and Applied Analysis
Volume18
Issue number3
DOIs
StatePublished - May 2019

Keywords

  • Contracting rectangle
  • Ikehara’s Theorem
  • Lower solutions
  • non-monotone traveling wave solutions
  • Schauder’s fixed point theorem
  • Upper

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