Stability of OP oscillations and working memory capacity.

Abstract

For fixed τn, there is a window of τi values for which oscillations exist. We examine the existence and stability of the active out-of-phase populations, corresponding to distinct, single-featured memoranda. (A) Here, we look at the 3-OP state for a network of N = 5 populations, with τn fixed at 144 and the mutual inhibition cei fixed at 0.03. For τi too large or too small, the oscillations are lost as folds of limit cycles (for larger N, they may also be lost through torus or period-doubling bifurcations). (B) By following the limit points in (A) and keeping N fixed at 5, we may examine the dependence of the oscillatory states on both timescales, τn and τi, for different OP states. Thus, we see how the capacity of the system depends on the timescales. Each curve is a curve of the limit points as shown in (A). Thus, the OP state with 2 active populations exists stably above the blue curve, and the 3-OP state exists stably above the black curve. (C) We may further examine how the capacity is affected by the strength of the mutual inhibition, cei. Here, the 3-OP state exists above each curve for different cei values as indicated. As the mutual inhibition increases, the minimum τn value that supports the 3-OP state increases. Thus, we would like to keep the mutual inhibition low enough to support the 3-OP state within physiologically realistic synaptic timescales, but high enough to allow for the WTA state. (D) If we fix cei = 0.03, we may further explore how the network size N affects the 3-OP state. Overall, as N increases, the set of timescales that supports the 3-OP state does not change very much, generally increasing slightly. The bifurcation structure for N = 20 changes somewhat as well, so that the 3-OP state may destabilize through a torus or period-doubling bifurcation for lower τi values as well.</p