  Analytical analysis of spatially extended autocatalytic and hypercyclic
systems is presented. It is shown that spatially explicit systems in the form
of reaction-diffusion equations with global regulation possess the same major
qualitative features as the corresponding local models. In particular, using
the introduced notion of the stability in the mean integral sense we prove the
competitive exclusion principle for the autocatalytic system and the permanence
for the hypercycle system. Existence and stability of stationary solutions are
studied. For some parameter values it is proved that stable spatially
non-uniform solutions appear.
