  A Potts associative memory network has been proposed as a simplified model of
macroscopic cortical dynamics, in which each Potts unit stands for a patch of
cortex, which can be activated in one of S local attractor states. The internal
neuronal dynamics of the patch is not described by the model, rather it is
subsumed into an effective description in terms of graded Potts units, with
adaptation effects both specific to each attractor state and generic to the
patch. If each unit, or patch, receives effective (tensor) connections from C
other units, the network has been shown to be able to store a large number p of
global patterns, or network attractors, each with a fraction a of the units
active, where the critical load p_c scales roughly like p_c ~ (C S^2)/(a
ln(1/a)) (if the patterns are randomly correlated). Interestingly, after
retrieving an externally cued attractor, the network can continue jumping, or
latching, from attractor to attractor, driven by adaptation effects. The
occurrence and duration of latching dynamics is found through simulations to
depend critically on the strength of local attractor states, expressed in the
Potts model by a parameter w. Here we describe with simulations and then
analytically the boundaries between distinct phases of no latching, of
transient and sustained latching, deriving a phase diagram in the plane w-T,
where T parametrizes thermal noise effects. Implications for real cortical
dynamics are briefly reviewed in the conclusions.
