Delays and tori in a nonlinear model from motor control

Sue Ann Campbell; Jacques Belair

doi:10.1117/12.162719

5 November 1993 Delays and tori in a nonlinear model from motor control

Sue Ann Campbell, Jacques Belair

Proceedings Volume 2036, Chaos in Biology and Medicine; (1993) https://doi.org/10.1117/12.162719
Event: SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, 1993, San Diego, CA, United States

Abstract

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.

Citation Download Citation

Sue Ann Campbell and Jacques Belair "Delays and tori in a nonlinear model from motor control", Proc. SPIE 2036, Chaos in Biology and Medicine, (5 November 1993); https://doi.org/10.1117/12.162719

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available