  Through multiple-scales and symmetry arguments we derive a model set of
amplitude equations describing the interaction of two steady-state
pattern-forming instabilities, in the case that the wavelengths of the
instabilities are nearly in the ratio 1:2. In the case of exact 1:2 resonance
the amplitude equations are ODEs; here they are PDEs.
  We discuss the stability of spatially-periodic solutions to long-wavelength
disturbances. By including these modulational effects we are able to explore
the relevance of the exact 1:2 results to spatially-extended physical systems
for parameter values near to this codimension-two bifurcation point. These new
instabilities can be described in terms of reduced `normal form' PDEs near
various secondary codimension-two points. The robust heteroclinic cycle in the
ODEs is destabilised by long-wavelength perturbations and a stable periodic
orbit is generated that lies close to the cycle. An analytic expression giving
the approximate period of this orbit is derived.
