Existence of traveling wave solutions in a diffusive predator-prey model

Jianhua Huang, Gang Lu, Shigui Ruan

Research output: Contribution to journalArticle

78 Citations (Scopus)

Abstract

We establish the existence of traveling front solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-II functional response. The traveling front solutions are equivalent to heteroclinic orbits in R 4 and the small amplitude traveling wave train solutions are equivalent to small amplitude periodic orbits in R4. The methods used to prove the results are the shooting argument and the Hopf bifurcation theorem.

Original languageEnglish (US)
Pages (from-to)132-152
Number of pages21
JournalJournal of Mathematical Biology
Volume46
Issue number2
DOIs
StatePublished - Feb 2003

Fingerprint

Predator-prey Model
Traveling Wave Solutions
Travelling Fronts
predators
orbits
Orbit
Heteroclinic Orbit
Orbits
Functional Response
Shooting
Reaction-diffusion System
Hopf Bifurcation
Periodic Orbits
Hopf bifurcation
functional response models
Theorem
methodology

Keywords

  • Hopf bifurcation
  • Shooting argument
  • Traveling wave solution
  • Wazewski set

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Mathematics (miscellaneous)

Cite this

Existence of traveling wave solutions in a diffusive predator-prey model. / Huang, Jianhua; Lu, Gang; Ruan, Shigui.

In: Journal of Mathematical Biology, Vol. 46, No. 2, 02.2003, p. 132-152.

Research output: Contribution to journalArticle

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