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 language||American English|
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|Issue number||2 2|
|State||Published - 1 Jan 2004|