Time Scale Hierarchies in the Functional Organization of Complex Behaviors
Figure 6
From top to bottom: means and standard deviations of y(t) (denoted as yµ(t) and ys(t)) of dy(t)/dt ((dy/dt)µ(t), and (dy/dt)s(t)), of δy(t) (δyµ(t) and δys(t)), of z(t) (z µ(t) and z s(t)) of dz(t)/dt ((dz/dt)µ(t), and (dz/dt)s(t)), of δz(t) (δzµ(t) and δzs(t)), and of {ξj(t)} (ξj µ(t) and ξj s(t)). Means are plotted in blue and standard deviations in green except for the graph of {ξj(t)} where colors correspond to different modes and where means and standard deviations are plotted with a continuous and dashed line, respectively. Grey and pink shadings focus on the segments of increased {ξj(t)} and δy,z(t) variability, respectively. Notice the strong effect of δ-‘kicks’ on the means and standard deviations of the state variables' rates of change ((dy/dt)µ(t), dz/dt)µ(t) and (dy/dt)s(t), (dz/dt)s(t)). Instead, the variability of {ξj(t)} (ξjs(t)) has a much weaker effect on (dy/dt)s(t) and (dz/dt)s(t), and cannot be unambiguously distinguished from the rest of the (dy/dt)s(t) and (dz/dt)s(t) variability.