Strong nonlocal coupling stabilizes localized structures: An analysis based on front dynamics

C. Fernandez-Oto, M. G. Clerc, D. Escaff, M. Tlidi

Research output: Contribution to journalArticlepeer-review

41 Scopus citations

Abstract

We investigate the effect of strong nonlocal coupling in bistable spatially extended systems by using a Lorentzian-like kernel. This effect through front interaction drastically alters the space-time dynamics of bistable systems by stabilizing localized structures in one and two dimensions, and by affecting the kinetics law governing their behavior with respect to weak nonlocal and local coupling. We derive an analytical formula for the front interaction law and show that the kinetics governing the formation of localized structures obeys a law inversely proportional to their size to some power. To illustrate this mechanism, we consider two systems, the Nagumo model describing population dynamics and nonlinear optics model describing a ring cavity filled with a left-handed material. Numerical solutions of the governing equations are in close agreement with analytical predictions.
Original languageAmerican English
JournalPhysical Review Letters
Volume110
Issue number17
DOIs
StatePublished - 22 Apr 2013

Fingerprint Dive into the research topics of 'Strong nonlocal coupling stabilizes localized structures: An analysis based on front dynamics'. Together they form a unique fingerprint.

Cite this