[en] 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.
Disciplines :
Mathematics
Author, co-author :
Franci, Alessio ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Systèmes et modélisation ; Department of Mathematics, Universidad Nacional Autónoma de México (UNAM), Ciudad de México, Mexico
Sepulchre, Rodolphe; Department of Engineering, University of Cambridge, Cambridge, United Kingdom
Language :
English
Title :
A three-scale model of spatio-temporal bursting
Publication date :
2016
Journal title :
SIAM Journal on Applied Dynamical Systems
eISSN :
1536-0040
Publisher :
Society for Industrial and Applied Mathematics Publications
UNAM - Universidad Nacional Autónoma de México ERC - European Research Council
Funding text :
The research leading to these results has received funding from the European Research Council under the Advanced ERC Grant Agreement Switchlet 670645 and from DGAPA-Universidad Nacional Autónoma de México under the PAPIIT Grant IA105816.
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