Time Scale Hierarchies in the Functional Organization of Complex Behaviors
Figure 4
Simulation of the functional architecture generating the word ‘flow’.
Panel A shows the generation of the word ‘flow’ and the operational signals involved. The word is repetitively generated after a short transient (black solid line). Four principle functional modes are used, one for each character (associated with solid blue, green, magenta and cyan lines, respectively), plus two auxiliary ones at the sequence's beginning and end (dotted dark and light brown lines, respectively). From top to bottom: three repetitions of the word in the handwriting workspace (the plane x-y), the output trajectory in the 3-dimensional functional phase space spanned by state variables x, y and z, followed by their time series, and the time series of the slow (WTA competition coefficients {|ξj|}) and the instantaneous (δy,z ‘kicks’, light and dark red, respectively) operational signals. The {ξj} of the modes that do not participate in the word always have a value close to zero (red line). Panel B shows the feedback loop from the output dynamics to the slow sequential one. From top to bottom: time series of the inhibitory feedback functions Fjinh, the slow feedback integrating variables vj, the absolute values of the (fast) ‘switching’ variables λj, and the WTA competition parameters Cj and Lj. These quantities vary on the time scale of a whole word (except for Fjinh that varies at the time scale of a movement cycle), even if they also contain fast changes during their evolution. The parameter values for this simulation were as follows: noise standard deviation was s = 0.001, while kjinh = [6,12,5,5,2.67,6] and kjexc = [12], [11], [10], [9], [8], [7] for each mode in the sequence, respectively (only these parameters that have to be manually set prior to a simulation). The initial conditions for the functional mode dynamics were x0 = 0, y0 = 0.1, and z0 = −0.1, while those of {νj}, {λj} and {ξj} where chosen randomly from a uniform distribution in the interval [0,1] for {νj} and {λj}, and [0,1/K] for {ξj}.