A three-scale model of spatio-temporal bursting
Dynamical Systems
2016-07-12 v2 Analysis of PDEs
Pattern Formation and Solitons
Abstract
We study spatio-temporal bursting in a three-scale reaction diffusion equation organized by the winged cusp singularity. For large time-scale separation the model exhibits traveling bursts, whereas for large space-scale separation the model exhibits standing bursts. Both behaviors exhibit a common singular skeleton, whose geometry is fully determined by persistent bifurcation diagrams of the winged cusp. The modulation of spatio-temporal bursting in such a model naturally translates into paths in the universal unfolding of the winged-cusp.
Cite
@article{arxiv.1510.08938,
title = {A three-scale model of spatio-temporal bursting},
author = {Alessio Franci and Rodolphe Sepulchre},
journal= {arXiv preprint arXiv:1510.08938},
year = {2016}
}