Analytical approach to localized structures in a simple reaction-diffusion system

Orazio Descalzi*, Yumino Hayase, Helmut R. Brand

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


A simple reaction-diffusion model, which admits stable oscillating localized structures is discussed. The approximate analytical expressions for localized oscillating structures in the reaction-diffusion model are calculated using a generalized matching approach. It is found that the oscillating particlelike solutions lead to the traveling waves generation in the phase because the limit cycle is not a circle. Results show that the analytical approximation captures all the essential ingredients of these breathing particlelike solutions.

Original languageEnglish
Article number026121
Pages (from-to)026121-1-026121-9
JournalPhysical Review E
Issue number2 2
StatePublished - Feb 2004


  • Diffusion
  • Models, Statistical
  • Models, Theoretical
  • Oscillometry
  • Physical Phenomena
  • Physics
  • Systems Theory


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