  We consider the multitasking associative network in the low-storage limit and
we study its phase diagram with respect to the noise level $T$ and the degree
$d$ of dilution in pattern entries. We find that the system is characterized by
a rich variety of stable states, among which pure states, parallel retrieval
states, hierarchically organized states and symmetric mixtures (remarkably,
both even and odd), whose complexity increases as the number of patterns $P$
grows. The analysis is performed both analytically and numerically: Exploiting
techniques based on partial differential equations, allows us to get the
self-consistencies for the order parameters. Such self-consistence equations
are then solved and the solutions are further checked through stability theory
to catalog their organizations into the phase diagram, which is completely
outlined at the end. This is a further step toward the understanding of
spontaneous parallel processing in associative networks.
