Locating the transition from periodic oscillations to spatiotemporal chaos in the wake of invasion

Jonathan A. Sherratt, Matthew J. Smith, J. D M Rademacher

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

In systems with cyclic dynamics, invasions often generate periodic spatiotemporal oscillations, which undergo a subsequent transition to chaos. The periodic oscillations have the form of a wavetrain and occur in a band of constant width. In applications, a key question is whether one expects spatiotemporal data to be dominated by regular or irregular oscillations or to involve a significant proportion of both. This depends on the width of the wavetrain band. Here,wepresent mathematical theory that enables the direct calculation of this width. Our method synthesizes recent developments in stability theory and computation. It is developed for only 1 equation system, but because this is a normal form close to a Hopf bifurcation, the results can be applied directly to a wide range of models. We illustrate this by considering a classic example from ecology: wavetrains in the wake of the invasion of a prey population by predators.

Original languageEnglish
Pages (from-to)10890-10895
Number of pages6
JournalProceedings of the National Academy of Sciences
Volume106
Issue number27
DOIs
Publication statusPublished - 7 Jul 2009

Keywords

  • Absolute stability
  • Complex Ginzburg-Landau equation
  • Periodic travelling wave
  • Predator-prey
  • Reaction-diffusion

Fingerprint Dive into the research topics of 'Locating the transition from periodic oscillations to spatiotemporal chaos in the wake of invasion'. Together they form a unique fingerprint.

Cite this