A three-scale model of spatio-temporal bursting

Geometric singular perturbation theory; Reaction diffusion; Singularity theory; Spatio-temporal bursting; Bifurcation diagram; Reaction diffusion equations; Spatio temporal; Time scale separation; Universal unfolding; Analysis; Modeling and Simulation

Abstract :

[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

Volume :

Issue :

Pages :

2143 - 2175

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

http://epubs.siam.org/doi/pdf/10.1137/15M1046101

Funders :

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.

Available on ORBi :

since 26 May 2023

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