We study latching dynamics in the adaptive Potts model network, through numerical simulations with randomly and also weakly correlated patterns, and we focus on comparing its slowly and fast adapting regimes. A measure,

*Q*, is used to quantify the

*quality of latching* in the phase space spanned by the number of Potts states

*S*, the number of connections per Potts unit

*C* and the number of stored memory patterns

*p*. We find narrow regions, or

*bands* in phase space, where distinct pattern retrieval and duration of latching combine to yield the highest values of

*Q*. The bands are confined by the storage capacity curve, for large

*p*, and by the onset of finite latching, for low

*p*. Inside the band, in the slowly adapting regime, we observe complex structured dynamics, with transitions at high crossover between correlated memory patterns; while away from the band latching, transitions lose complexity in different ways: below, they are clear-cut but last such few steps as to span a transition matrix between states with few asymmetrical entries and limited entropy; while above, they tend to become random, with large entropy and bi-directional transition frequencies, but indistinguishable from noise. Extrapolating from the simulations, the band appears to scale almost quadratically in the

*p*–

*S* plane, and sublinearly in

*p*–

*C*. In the fast adapting regime, the band scales similarly, and it can be made even wider and more robust, but transitions between anti-correlated patterns dominate latching dynamics. This suggest that slow and fast adaptation have to be integrated in a scenario for viable latching in a cortical system. The results for the slowly adapting regime, obtained with randomly correlated patterns, remain valid also for the case with correlated patterns, with just a simple shift in phase space.

Full article