Breathing dissipative solitons in three-component reaction-diffusion system.
We investigate the stability of the localized stationary solutions of a three-component reaction-diffusion system with one activator and two inhibitors. A change of the time constants of the inhibitors can lead to a destabilization of the stationary solution. The special case we are interested in is that the breathing mode becomes unstable first and the stationary dissipative soliton undergoes a bifurcation from a stationary to a "breathing" state. This situation is analyzed performing a two-time-scale expansion in the vicinity of the bifurcation point thereby obtaining the corresponding amplitude equation. Also numerical simulations are carried out showing good agreement with the analytical predictions.
Gurevich
S V
SV
Institut für Angewandte Physik, Corrensstr. 2/4, D-48149 Münster, Germany.
Amiranashvili
Sh
Sh
Purwins
H-G
HG