We present a simple reaction-diffusion model for two variables. The model was originally designed to have a stable localized solution for a range of parameters as a consequence of the coexistence of a stable limit cycle and a stable fixed point. We classify the spatially homogeneous solutions of the model. In addition we describe several bifurcation scenarios for particle-like solutions as a function of two of the parameters.
|Number of pages||6|
|Journal||Physica A: Statistical Mechanics and its Applications|
|State||Published - 1 Oct 2005|
|Event||Nonequilibrium Statistical Mechanics and Nonlinear Physics (MEDYFINOL'04) - |
Duration: 2 Dec 2004 → 4 Dec 2004
Bibliographical noteFunding Information:
Y.H. thanks the Alexander von Humboldt-Foundation for partial support. O.D. thanks the Fondecyt (Project 1050660) and FAI (Universidad de los Andes, Project ICIV-001-04) for financial support. H.R.B. thanks the Deutsche Forschungsgemeinschaft for partial support through SFB 481: Polymere und Hybridmaterialien in inneren und äußeren Feldern.
- Limit cycles
- Localized solutions
- Particle solutions
- Reaction-diffusion systems