TY - JOUR
T1 - Resonant forcing of chaotic dynamics
AU - Gintautas, Vadas
AU - Foster, Glenn
AU - Hübler, Alfred W.
N1 - Funding Information:
Acknowledgements The authors thank U.H. Gerlach for useful discussions concerning inhomogeneous eigenvalue problems and S. Raymond for other helpful input. This work was supported by the National Science Foundation Grant Nos. NSF PHY 01-40179, NSF DMS 03-25939 ITR, and NSF DGE 03-38215.
Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2008/2
Y1 - 2008/2
N2 - We study resonances of multidimensional chaotic map dynamics. We use the calculus of variations to determine the additive forcing function that induces the largest response, that is, the greatest deviation from the unperturbed dynamics. We include the additional constraint that only select degrees of freedom be forced, corresponding to a very general class of problems in which not all of the degrees of freedom in an experimental system are accessible to forcing. We find that certain Lagrange multipliers take on a fundamental physical role as the efficiency of the forcing function and the effective forcing experienced by the degrees of freedom which are not forced directly. Furthermore, we find that the product of the displacement of nearby trajectories and the effective total forcing function is a conserved quantity. We demonstrate the efficacy of this methodology with several examples.
AB - We study resonances of multidimensional chaotic map dynamics. We use the calculus of variations to determine the additive forcing function that induces the largest response, that is, the greatest deviation from the unperturbed dynamics. We include the additional constraint that only select degrees of freedom be forced, corresponding to a very general class of problems in which not all of the degrees of freedom in an experimental system are accessible to forcing. We find that certain Lagrange multipliers take on a fundamental physical role as the efficiency of the forcing function and the effective forcing experienced by the degrees of freedom which are not forced directly. Furthermore, we find that the product of the displacement of nearby trajectories and the effective total forcing function is a conserved quantity. We demonstrate the efficacy of this methodology with several examples.
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U2 - 10.1007/s10955-007-9444-4
DO - 10.1007/s10955-007-9444-4
M3 - Article
AN - SCOPUS:37549034594
SN - 0022-4715
VL - 130
SP - 617
EP - 629
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 3
ER -