First row: each plot presents three snapshots of the network activity at three different times (t1, t2 and t3), for a system encoding a one dimensional (a), two dimensional (b) and three dimensional (c) manifold. In (c), activity is color-coded (blue represents low activity, red is high activity, silent neurons are not plotted for better readability). In all cases, the anti-symmetric component is oriented along the x axis. (d) Dependence of the speed on γ and . Dots are data from numerical simulations, full lines are the fitted curves. (e) Retrieval of two crossing trajectories. Black arrows represent the two intersecting encoded trajectories, each parallel to one of the axis. Full colored lines show the trajectories actually followed by the center of mass of the activity from the same starting point. Blue curve: low γ, the activity switches trajectories when it reaches the crossing point. Orange curve: high γ, successful crossing. In both cases . The blue and the orange insets show the activity bumps in the corresponding cases; the top-right inset shows the dependence of the value , required for crossing, on ξ.