TY - JOUR
T1 - Analytical approach to localized structures in a simple reaction-diffusion system
AU - Descalzi, Orazio
AU - Hayase, Yumino
AU - Brand, Helmut R.
PY - 2004/1/1
Y1 - 2004/1/1
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevE.69.026121
DO - 10.1103/PhysRevE.69.026121
M3 - Article
VL - 69
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
SN - 1063-651X
IS - 2 2
ER -