A modular latching chain.

Many cognitive tasks involve transitions between distinct mental processes, which may range from discrete states to complex strategies. The ability of cortical networks to combine discrete jumps with continuous glides along ever changing trajectories, dubbed latching dynamics, may be essential for the emergence of the unique cognitive capacities of modern humans. Novel trajectories have to be followed in the multidimensional space of cortical activity for novel behaviours to be produced; yet, not everything changes: several lines of evidence point at recurring patterns in the sequence of activation of cortical areas in a variety of behaviours. To extend a mathematical model of latching dynamics beyond the simple unstructured auto-associative Potts network previously analysed, we introduce delayed structured connectivity and hetero-associative connection weights, and we explore their effects on the dynamics. A modular model in the small-world regime is considered, with modules arranged on a ring. The synaptic weights include a standard auto-associative component, stabilizing distinct patterns of activity, and a hetero-associative component, favoring transitions from one pattern, expressed in one module, to the next, in the next module. We then study, through simulations, how structural parameters, like those regulating rewiring probability, noise and feedback connections, determine sequential association dynamics.