Dynamics of one- and two-dimensional fronts in a bistable equation with time-delayed global feedback: Propagation failure and control mechanisms

Document Type

Article

Publication Date

9-2-2010

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. © 2010 The American Physical Society.

Identifier

77957195703 (Scopus)

Publication Title

Physical Review E Statistical Nonlinear and Soft Matter Physics

External Full Text Location

https://doi.org/10.1103/PhysRevE.82.036601

e-ISSN

15502376

ISSN

15393755

Issue

3

Volume

82

Grant

0817241

Fund Ref

National Science Foundation

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