Discrete Vortices in Systems of Coupled Nonlinear Oscillators: Numerical Results for an Electric Model

Abstract

Vortex coherent structures on arrays of nonlinear oscillators joined by weak links into topologically nontrivial two-dimensional discrete manifolds have been theoretically studied. A circuit of nonlinear electric oscillators coupled by relatively weak capacitances has been considered as a possible physical implementation of such objects. Numerical experiments have shown that a time-monochromatic external force applied to several oscillators leads to the formation of long-lived and nontrivially interacting vortices in the system against a quasistationary background in a wide range of parameters. The dynamics of vortices depends on the method of "coupling" of the opposite sides of a rectangular array by links, which determines the topology of the resulting manifold (torus, Klein bottle, projective plane, M\"obius strip, ring, or disk).