Time Scale Hierarchies in the Functional Organization of Complex Behaviors
Figure 2
Functional modes and architecture overview.
Interactions among functional modes Fj({ui}) result in one of them dominating the output of the functional architecture for a period of time followed by the domination of another one via a fast transient. Three modes (associated with different colors) of the available dynamic repertoire are shown. They all correspond to 2-dimensional phase flows on an ellipsoid manifold. Blue represents a monostable phase flow, magenta a limit cycle flow, and green a bistable flow. Their vector field and a set of characteristic trajectories starting from different initial conditions (small asterisks) are shown. The modes' mutual interactions are depicted as bidirectional couplings (arrows) among their associated weighting coefficients {ξj(t)} (with which they have a multiplicative relationship). The resulting expressed phase flow F({ui},t) (shown as a trajectory in the phase space and time) results from their linear combination at each time moment, while {ui(t)} is the respective time series. {ξj(t)} play the role of a slow operating signal (with respect to the inherent time scale of the functional modes, i.e., τξ>>τf). Finally, an instantaneous (τδ<<τf) operational signal {δi(t)} (in red) may have an additive contribution to F({ui},t), acting like a meaningful perturbation.