Dresden 2009 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 17: Reaction-diffusion systems

DY 17.2: Talk

Wednesday, March 25, 2009, 15:00–15:15, ZEU 118

Moving and breathing dissipative solitons in a three-component reaction-diffusion system — •Svetlana Gurevich and Rudolf Friedrich — Institute for Theoretical Physics, WWU Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany

We are interested in the stability of the stationary localized structures (so-called dissipative solitons) in a three-component reaction-diffusion system with one activator and two inhibitors. Changing the time constants of inhibitors can lead to various destabilizations of the stationary dissipative soliton. In many cases the breathing mode becomes unstable first and the stationary dissipative soliton undergoes a bifurcation from a stationary to a breathing state. On the other hand a mode responding to a movement can be unstable first and a drift-bifurcation takes a place. Here we are interested in the interaction between these two unstable modes. This situation is analyzed performing a multiple scale perturbation expansion in the vicinity of the codim 2 bifurcation point and the corresponding amplitude equation is obtained. Also numerical simulations are carried out showing good agreement with the analytical predictions.