Journal of Statistical Physics

, Volume 130, Issue 3, pp 617–629 | Cite as

Resonant Forcing of Chaotic Dynamics

  • Vadas Gintautas
  • Glenn Foster
  • Alfred W. Hübler
Article
First Online:
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Accepted:

Abstract

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.

Keywords

Lagrange Multiplier Jacobi Matrix Nonlinear Oscillator Stat Phys Force Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Vadas Gintautas
    • 1
  • Glenn Foster
    • 1
  • Alfred W. Hübler
    • 1
  1. 1.Center for Complex Systems Research, Department of PhysicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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