Publication: Theoretical analysis of destabilization resonances in time-delayed stochastic second-order dynamical systems and some implications for human motor control
2
Issued Date
2006-03-02
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ISSN
15502376
15393755
15393755
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2-s2.0-33344463083
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Mahidol University
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SCOPUS
Bibliographic Citation
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. Vol.73, No.2 (2006)
Suggested Citation
K. Patanarapeelert, T. D. Frank, R. Friedrich, P. J. Beek, I. M. Tang Theoretical analysis of destabilization resonances in time-delayed stochastic second-order dynamical systems and some implications for human motor control. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. Vol.73, No.2 (2006). doi:10.1103/PhysRevE.73.021901 Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/23398
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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
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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.