Discrete vortices on spatially nonuniform two-dimensional electric networks

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.