  Long-period EUV pulsations, recently discovered to be common in active
regions, are understood to be the coronal manifestation of thermal
non-equilibrium (TNE). The active regions previously studied with EIT/SOHO and
AIA/SDO indicated that long-period intensity pulsations are localized in only
one or two loop bundles. The basic idea of this study is to understand why. For
this purpose, we tested the response of different loop systems, using different
magnetic configurations, to different stratifications and strengths of the
heating. We present an extensive parameter-space study using 1D hydrodynamic
simulations (1,020 in total) and conclude that the occurrence of TNE requires
specific combinations of parameters. Our study shows that the TNE cycles are
confined to specific ranges in parameter space. This naturally explains why
only some loops undergo constant periodic pulsations over several days: since
the loop geometry and the heating properties generally vary from one loop to
another in an active region, only the ones in which these parameters are
compatible exhibits TNE cycles. Furthermore, these parameters (heating and
geometry) are likely to vary significantly over the duration of a cycle, which
potentially limits the possibilities of periodic behavior. This study also
confirms that long-period intensity pulsations and coronal rain are two aspects
of the same phenomenon: both phenomena can occur for similar heating conditions
and can appear simultaneously in the simulations.
