Nonlocal feedback in nonlinear systems

TL;DR

This paper explores how nonlocal feedback loops in nonlinear systems induce unique spatial and temporal behaviors, including instabilities and perturbation dynamics, with analytical insights into their complex spatio-temporal evolution.

Contribution

It introduces the concept of nonlocal feedback as a spatial analog of delay, analyzing its effects on system dynamics in various dimensions and noise conditions.

Findings

Nonlocal feedback causes convective instabilities.

Independent tuning of phase and group velocities is possible.

Localized perturbations can be amplified, chirped, or split.

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.