Discrete vortices on spatially nonuniform two-dimensional electric networks

Two-dimensional arrays of nonlinear electric oscillators are considered theoretically where nearest neighbors are coupled by relatively small constant but nonequal capacitors. The dynamics is approximately reduced to a weakly dissipative defocusing discrete nonlinear Schrödinger equation with translationally noninvariant linear dispersive coefficients. Behavior of quantized discrete vortices in such systems is shown to depend strongly on the spatial profile of the internode coupling as well as on the ratio between time-increasing healing length and lattice spacings. In particular, vortex clusters can be stably trapped for 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.