  We consider suppression of macroscopic synchronized oscillations in mixed
populations of active and inactive oscillators with local diffusive coupling,
described by a lattice complex Ginzburg-Landau model with discrete Laplacian in
general dimensions. Approximate expression for the stability of the
non-oscillatory stationary state is derived on the basis of the generalized
free energy of the system. We show that an effective wavenumber of the system
determined by the spatial arrangement of the active and inactive oscillators is
an decisive factor in the suppression, in addition to the ratio of active
population to inactive population and relative intensity of each population.
The effectiveness of the proposed theory is illustrated with a cortico-thalamic
model of epileptic seizures, where active and inactive oscillators correspond
to epileptic foci and healthy cerebral cortex tissue, respectively.
