  Motivated by the impact of worsening climate conditions on vegetation
patches, we study dynamic instabilities in an idealized Ginzburg-Landau model.
Our main results predict time instances of sudden drops in wavenumber and the
resulting target states. The changes in wavenumber correspond to the
annihilation of individual vegetation patches when resources are scarce and
cannot support the original number of patches. Drops happen well after the
primary pattern has destabilized at the Eckhaus boundary and key to
distinguishing between the disappearance of 1,2, or more patches during the
drop are complex spatio-temporal resonances in the linearization at the
unstable pattern. We support our results with numerical simulations and expect
our results to be conceptually applicable universally near the Eckhaus
boundary, in particular in more realistic models.
