Moving and Breathing Localized Structures in Reaction-diffusion Systems

Institut for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, 48149, Münster, Germany

^⋆ Corresponding author. E-mail: gurevics@uni-muenster.de

Abstract

We are interested in the stability of the localized stationary solutions of a three-component reaction-diffusion system with one activator and two inhibitors. We show that depending on control parameters, solutions in form of moving and breathing localized structures can be observed in the vicinity of the codimension-two bifurcation point. We analyze this situation performing multiple scale perturbation expansion in the vicinity of the bifurcation point and derive a set of order parameter equations, explicitly describing the dynamics of the single localized structure. Numerical simulations are carried out, showing good agreement with the analytical predictions.