| We investigate stability of the localized stationary solutions in a three-component reaction-diffusion system with one activator and two inhibitors. Change of the time constants of inhibitors can lead to 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 and the corresponding amplitude equation is obtained. Also numerical simulations are carried out showing good agreement with the analytical predictions. |
|