Dynamics of one- and two-dimensional fronts in a bistable equation with time-delayed global feedback : propagation failure and control mechanisms
Boubendir, Yassine (New Jersey Institute of Technology. Department of Mathematical Sciences)
Méndez López, Vicenç (Universitat Autònoma de Barcelona. Departament de Física)
Rotstein, Horacio G. (New Jersey Institute of Technology. Department of Mathematical Sciences)

Date:	2010
Abstract:	We study the evolution of fronts in a bistable equation with time-delayed global feedback in the fast reaction and slow diffusion regime. This equation generalizes the Hodgkin-Grafstein and Allen-Cahn equations. We derive a nonlinear equation governing the motion of fronts, which includes a term with delay. In the one-dimensional case this equation is linear. We study the motion of one- and two-dimensional fronts, finding a much richer dynamics than for the previously studied cases (without time-delayed global feedback). We explain the mechanism by which localized fronts created by inhibitory global coupling loose stability in a Hopf bifurcation as the delay time increases. We show that for certain delay times, the prevailing phase is different from that corresponding to the system in the absence of global coupling. Numerical simulations of the partial differential equation are in agreement with the analytical predictions.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Published in:	Physical review. E : Statistical, nonlinear, and soft matter physics, Vol. 82, Number 3 (September 2010) , p. 036601/1-036601/20, ISSN 1539-3755

DOI: 10.1103/PhysRevE.82.036601

20 p, 1.8 MB

The record appears in these collections:
Articles > Research articles
Articles > Published articles