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Title: Theoretical analysis of destabilization resonances in time-delayed stochastic second-order dynamical systems and some implications for human motor control
Authors: K. Patanarapeelert
T. D. Frank
R. Friedrich
P. J. Beek
I. M. Tang
Mahidol University
Westfalische Wilhelms-Universitat Munster
Vrije Universiteit Amsterdam
Keywords: Mathematics;Physics and Astronomy
Issue Date: 2-Mar-2006
Citation: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. Vol.73, No.2 (2006)
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. © 2006 The American Physical Society.
ISSN: 15502376
Appears in Collections:Scopus 2006-2010

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