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Network mechanisms underlying the role of oscillations in cognitive tasks

Fig 2

Switching behavior at the macroscopic scale.

A Bifurcation analysis of the stationary states identifies a bistable regime for large enough J where a stable focus (red) and a stable node (blue) coexist, separated by a saddle (dotted green). The color-coded curve represents the bifurcation diagram for the value of used here, and the grey curves represent the bifurcation diagrams at different values (left to right: 4J/3, 2J/3, J/3). B The different dynamic regimes of the forced system are shown here as a function of the amplitude A and the frequency f of the forcing. Green: Recall; Red: Clearance; Grey: no switching. Orange: only one globally stable periodic orbit exists due to the system being entrained to the forcing, hysteretically switching between the node and the focus. C Example time traces from B, with initial conditions chosen to be the focus (red) or the node (blue). D The heuristic firing-rate equations Eq 4 show an equivalent fixed point structure, with the exception that the focus is a node here. E Clearance does not occur in the firing-rate equations, as the node cannot be destabilized by nonlinear resonance. Parameters: τ = 20ms, η = −10, Δ = 2, , A = 1.

doi: https://doi.org/10.1371/journal.pcbi.1006430.g002