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

Orazio Descalzi, Yumino Hayase, Helmut R. Brand

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Abstract

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 languageAmerican English
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume69
Issue number2 2
DOIs
StatePublished - 1 Jan 2004

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