A simple two-component reaction-diffusion system showing rich dynamic behavior: Spatially homogeneous aspects and selected bifurcation scenarios

Yumino Hayase, Orazio Descalzi, Helmut R. Brand

Research output: Contribution to journalConference articlepeer-review

7 Scopus citations

Abstract

We present a simple reaction-diffusion model for two variables. The model was originally designed to have a stable localized solution for a range of parameters as a consequence of the coexistence of a stable limit cycle and a stable fixed point. We classify the spatially homogeneous solutions of the model. In addition we describe several bifurcation scenarios for particle-like solutions as a function of two of the parameters.

Original languageEnglish
Pages (from-to)19-24
Number of pages6
JournalPhysica A: Statistical Mechanics and its Applications
Volume356
Issue number1
DOIs
StatePublished - 1 Oct 2005
EventNonequilibrium Statistical Mechanics and Nonlinear Physics (MEDYFINOL'04) -
Duration: 2 Dec 20044 Dec 2004

Bibliographical note

Funding Information:
Y.H. thanks the Alexander von Humboldt-Foundation for partial support. O.D. thanks the Fondecyt (Project 1050660) and FAI (Universidad de los Andes, Project ICIV-001-04) for financial support. H.R.B. thanks the Deutsche Forschungsgemeinschaft for partial support through SFB 481: Polymere und Hybridmaterialien in inneren und äußeren Feldern.

Keywords

  • Limit cycles
  • Localized solutions
  • Particle solutions
  • Reaction-diffusion systems

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