Existence of traveling waves for integral recursions with nonmonotone growth functions

Bingtuan Li, Mark A. Lewis, Hans F. Weinberger

Research output: Contribution to journalArticle

78 Scopus citations

Abstract

A class of integral recursion models for the growth and spread of a synchronized single-species population is studied. It is well known that if there is no overcompensation in the fecundity function, the recursion has an asymptotic spreading speed c*, and that this speed can be characterized as the speed of the slowest non-constant traveling wave solution. A class of integral recursions with overcompensation which still have asymptotic spreading speeds can be found by using the ideas introduced by Thieme (J Reine Angew Math 306:94-121, 1979) for the study of space-time integral equation models for epidemics. The present work gives a large subclass of these models with overcompensation for which the spreading speed can still be characterized as the slowest speed of a non-constant traveling wave. To illustrate our results, we numerically simulate a series of traveling waves. The simulations indicate that, depending on the properties of the fecundity function, the tails of the waves may approach the carrying capacity monotonically, may approach the carrying capacity in an oscillatory manner, or may oscillate continually about the carrying capacity, with its values bounded above and below by computable positive numbers.

Original languageEnglish (US)
Pages (from-to)323-338
Number of pages16
JournalJournal of Mathematical Biology
Volume58
Issue number3
DOIs
StatePublished - Mar 1 2009

Keywords

  • Integral recursion
  • Nonmonotone growth function
  • Spreading speed
  • Traveling waves

Fingerprint Dive into the research topics of 'Existence of traveling waves for integral recursions with nonmonotone growth functions'. Together they form a unique fingerprint.

  • Cite this