Time Scale Hierarchies in the Functional Organization of Complex Behaviors
Figure 7
From top to bottom: means and standard deviations of y (denoted as yµ and ys), of dy/dt ((dy/dt)µ and (dy/dt)s), of δy (δyµ and δys), of z (z µ and z s), of dz/dt ((dz/dt)µ and (dz/dt)s), of δz (δzµ and δzs), and of {ξj} (ξj µ and ξj s). Colors, shadings and line styles are similar as in Figure 6. The effect of δ-‘kicks’ on the architecture's output is as evident as in Figure 6 (notice also that (dy/dt)s and (dz/dt)s are almost identical to δys and δzs, respectively, in the segments with a δ-‘kick’). The variability of {ξj} (ξjs) that signals mode transitions, now has a significant effect on standard deviations of dy/dt and dz/dt that approximate the phase flow. This effect cannot be identified unambiguously in the variability of the trajectory in the phase space (ys and zs). At the first transition, the δ-‘kick’ variability follows that of the {ξj}, and their effects are easily separable. Instead, at the second transition, the mean of the {ξj} modulates the standard deviation of δz and thereby the one of dz/dt as well (because of their overlapping in the data set). At the third transition no δ-‘kick’ is involved; however, there is still a significant increase in (dy/dt)s and (dz/dt)s due to the increase in ξj s.