Citation

Patanarapeelert K, Frank TD, Friedrich R, Beek PJ, Tang IM. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2006; 73(2 Pt 1): 021901.

Affiliation

Faculty of Science, Department of Mathematics, Mahidol University, Rama VI Road, Bangkok 10400, Thailand.

Copyright

(Copyright © 2006, American Physical Society, Publisher American Institute of Physics)

DOI

unavailable

PMID

16605356

Abstract

A linear stochastic delay differential equation of second order is studied that can be regarded as a Kramers model with time delay. An analytical expression for the stationary probability density is derived in terms of a Gaussian distribution. In particular, the variance as a function of the time delay is computed analytically for several parameter regimes. Strikingly, in the parameter regime close to the parameter regime in which the deterministic system exhibits Hopf bifurcations, we find that the variance as a function of the time delay exhibits a sequence of pronounced peaks. These peaks are interpreted as delay-induced destabilization resonances arising from oscillatory ghost instabilities. On the basis of the obtained theoretical findings, reinterpretations of previous human motor control studies and predictions for future human motor control studies are provided.

Language: en