We consider linear nonautonomous second order parabolic equations
  on $R^N$. Under an instability condition, we prove the existence of
  two complementary Floquet bundles, one spanned by a positive entire
  solution - the principal Floquet bundle, the other one consisting of
  sign-changing solutions. We establish an exponential
  separation between the two bundles, showing in particular that
  a class of sign-changing solutions are exponentially dominated by
  positive solutions.