A model is derived for a `simple' motor control task. An artificial delay is introduced in the experiments to assess the dynamic influence it may have on normal and/or pathological conditions. The model takes the form of a delay-differential equation containing two time delays, associated with two (proprioceptive and visual) negative feedback loops. A linear stability analysis reveals a rich structure in the parameter values destabilizing the equilibrium. A nonlinear analysis, by a reduction on a center manifold when two Hopf bifurcations interact, reveals the existence of stable and unstable 2D tori. These results are contrasted with systems involving a single feedback loop, and a single time delay.
Sue Ann Campbell,
"Delays and tori in a nonlinear model from motor control", Proc. SPIE 2036, Chaos in Biology and Medicine, (5 November 1993); doi: 10.1117/12.162719; https://doi.org/10.1117/12.162719