FIG. 2.

Network in the marginally stable state functions as an integrator. (a) Sample traces from a network with switchlike update gates (α_z = 30, g_h = 3) show slow evolution (time on x axis is relative to τ_h). (b) An input is applied to the same network in (a) from t = 0 till t = 10, either aligned with a slow eigenvector u_λ (red traces) or unaligned with slow modes (black dashed trace). The plot shows the excess projection of the network state on the left eigenvector u_λ. Different shades of red correspond to different input strengths. If the input is along the slow manifold, the trace of the input is retained for a long time after the cessation of input. [The traces in (a) are for the network with an input along the manifold.].