  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).
