Localized Structures in Dissipative Nonlinear Systems - Abstract
Gurevich, Svetlana
We are interested in the stability of the nontrivial stationary solution (so-called dissipative soliton (DS)) of a three- component reaction-diffusion system. In the simplest case it is a stationary localized structure with rotational symmetry, which is stable in a certain parameter region. By changing system parameters single DS can lose their stability via e.g., a drift-bifurcation. Another example is a breathing bifurcation, leading to the oscillating in space DSs. Moreover, an interaction between these two unstable modes is possible, giving rise for a co-dimensional two bifurcation. These situations are analyzed performing a multiple scale perturbation expansion in the vicinity of the bifurcation points and the corresponding order parameter equations are obtained. Also numerical simulations are carried out showing good agreement with the analytical predictions.