Multitasking network with fast noise.

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 sys-tem is characterized by a rich variety of stable states, among which pure states, parallel retrieval states, hierarchically organized states and sym-metric mixtures (remarkably, both even and odd), whose complexity in-creases as the number of patterns P grows. The analysis is performed both analytically and numerically: Exploiting techniques based on par-tial 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 or-ganizations into the phase diagram, which is completely outlined at the end. This is a further step toward the understanding of spontaneous par-allel processing in associative networks.