Invading wave fronts and their oscillatory wakes are linked by a modulated travelling phase resetting wave

Research output: Contribution to journalArticle

52 Citations (Scopus)

Abstract

Periodic wave trains are the generic solution form for oscillatory reaction-diffusion equations in one space dimension. It has been shown previously that invasive wavefronts generate behind them a wave train with a different speed from that of the invasion [Sherratt, Physica D 70 (1994) 370-382]. In this paper, the mechanism of wave train generation is studied in detail for systems of two reaction-diffusion equations close to a supercritical Hopf bifurcation in the kinetics, with equal diffusion coefficients. A combination of analytical and numerical evidence is presented suggesting that the invasive front and wave train are separated by a modulated travelling wave of phase gradient, in which phase singularities occur periodically. This calculation leads to a prediction of the amplitude and speed of the wave train generated by invasion. Copyright © 1998 Elsevier Science B.V.

Original languageEnglish
Pages (from-to)145-166
Number of pages22
JournalPhysica D: Nonlinear Phenomena
Volume117
Issue number1-4
DOIs
Publication statusPublished - 1998

Keywords

  • Oscillatory systems
  • Reaction-diffusion
  • Travelling waves
  • Wave trains

Fingerprint Dive into the research topics of 'Invading wave fronts and their oscillatory wakes are linked by a modulated travelling phase resetting wave'. Together they form a unique fingerprint.

  • Cite this