Eur. Phys. J. D 58, 235-242 (2010)
https://doi.org/10.1140/epjd/e2010-00104-x

Nonlocal feedback in nonlinear systems

¹ IFISC (CSIC-UIB), Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain
² SUPA, Department of Physics, University of Strathclyde, 107 Rottenrow, Glasgow, G4 0NG, UK

Corresponding author: roberta@ifisc.uib-csic.es

Received: 8 January 2010
Revised: 5 March 2010
Published online: 26 April 2010

Abstract

A shifted or misaligned feedback loop gives rise to a two-point nonlocality that is the spatial analog of a temporal delay. Important consequences of this nonlocal coupling have been found both in diffusive and in diffractive systems, and include convective instabilities, independent tuning of phase and group velocities, as well as amplification, chirping and even splitting of localized perturbations. Analytical predictions about these nonlocal systems as well as their spatio-temporal dynamics are discussed in one and two transverse dimensions and in presence of noise.