Supplemental Materials A Limit-Cycle Self-Organizing Map Architecture for Stable Arm Control

To see how an input is encoded by a limit cycle after training, we take the open-loop spatial map as an example. Limit cycles on the other maps are qualitatively similar. The spatial map is provided with a spatial location X∗ for 2 time steps as afferent input. The activation parameter γ is fixed at 0 after training, meaning each non-winner has an activation value of 0 (inactive) while each winner has 1 (maximally activated). After the input is removed (αaff disabled for t ≥ 2), the activity of the map goes through a brief period of irregular aperiodic dynamics and eventually settles into a limit cycle attractor, a cyclically repeating sequence of activity patterns. This limit cycle is used as a representation of the corresponding afferent input, which, in this case, is the spatial location X∗. As indicated in Huang, Gentili, and Reggia (2014), similar inputs result in similar limit cycles. Fig. S1 shows a sample learned limit cycle of length 6 in the spatial map, where each activation pattern is sparsely coded.