Discrete vortices on spatially nonuniform two-dimensional electric networks

TL;DR

This paper theoretically investigates the behavior of discrete vortices in two-dimensional nonlinear electric oscillator arrays with nonuniform coupling, revealing how spatial profiles influence vortex stability and dynamics.

Contribution

It introduces a model of nonuniform coupled electric oscillators leading to a modified discrete nonlinear Schrödinger equation, analyzing vortex stability and dynamics in such systems.

Findings

Vortex behavior depends on the spatial coupling profile.

Vortex clusters can be temporarily trapped by a circular barrier.

Gradual dissipative broadening causes vortex destabilization and movement.

Abstract

Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly dissipative defocusing discrete nonlinear Schr\"odinger equation with translationally non-invariant linear dispersive coefficients. Behavior of quantized discrete vortices in such systems is shown to depend strongly on the spatial profile of the inter-node coupling as well as on the ratio between time-increasing healing length and lattice spacing. In particular, vortex clusters can be stably trapped for a some initial period of time by a circular barrier in the coupling profile, but then, due to gradual dissipative broadening of vortex cores, they lose stability and suddenly start to move.