It looks like it’s receiving the reference from the difference between cursor and target measures in terms of the difference in their phase and size. Is this the “oscillator” you’re talking about or is there an actual oscillator involved? I don’t see one in the diagram of the model.

It’s difficult to tell what’s going on in that inner loop. It looks like that loop is controlling a variable, x.dot, that is being added to the the current cursor position, c,x. The noise seems to be added to x.dot, not to c.x. If your subject is moving the cursor with a mouse or joystick then what the inner loop is doing is controlling the position of that mouse or joystick, protecting it from noise disturbances, which is a filtering process. But the filtering (in the model) is of x.dot, the output that affects the cursor, c.x, not the cursor movement itself.

By the way, in the paper you mention that you low-pass filtered the subject data for analysis. Did you compare the model to the filtered or raw subject data? I’ve found that I have to filter the subject data for analysis or the data has too many invalid data points due to brief segments in the movement where the cursor moves in a straight line.

Yes, of course, such as planetary orbits.

Look at the target trajectories in the two figures above. Perfect ellipse with constant speed has beta=0, with slight slowing down has beta=-1/3, and high slowing down is beta = -2/3. The model reproduces human behavior.

Beautiful! Exactly what I would expect. If you do the regression and include the affine velocity variable – Af = X.dot*Y.dot.dot - Y.dot*X.dot.dot – as a predictor you will see that the coefficient for the C predictor will be exactly -1/3 and for the Af predictor it will be exactly 1/3. And the R^2 for the regression will be 1.0.

This means that the degree to which you find a “power law” conforming coefficient for the relationship between V and C for any curved movement depends on the degree to which variations in Af are correlated with variations in C; the closer this correlation is to 0, the closer the power coefficient will be to its “lawful” value, -1/3. Since we typically find the power law coefficient to be about -1/3 plus or minus 1/7 for movements made by living systems, the interesting question to me seems to be what limits organisms to movements where Af has a low correlation with C.

How about trying the model on some different target movements…

How about reading the paper?

How about presenting it at the IAPCT conference?

RSM