Strong nonlocal coupling stabilizes localized structures: An analysis based on front dynamics
C. Fernandez-Oto, M. G. Clerc, D. Escaff, and M. Tlidi
Accepted
We investigate the effect of strong non-local 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 non-local 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.