Resonant forcing of select degrees of freedom of multidimensional chaotic map dynamics

@inproceedings{Gintautas2007ResonantFO,
  title={Resonant forcing of select degrees of freedom of multidimensional chaotic map dynamics},
  author={Vadas Gintautas and Glenn C. Foster and Alfred Wilhelm Hubler},
  year={2007}
}
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… Expand

Figures from this paper

References

SHOWING 1-10 OF 15 REFERENCES
Resonant forcing of multidimensional chaotic map dynamics.
TLDR
It is shown that resonant forcing functions of chaotic systems decrease exponentially, where the rate equals the negative of the largest Lyapunov exponent of the unperturbed system and the optimal forcing decreases rapidly and is only as effective as a single-push forcing. Expand
Resonances of nonlinear oscillators.
  • Wargitsch, Hübler
  • Physics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1995
TLDR
It is found that aperiodic driving forces are most effective for large nonlinearity and small friction and this optimal control is stable for several important systems. Expand
Dynamics of oscillators with periodic dichotomous noise
The dynamics of bistable oscillators driven by periodic dichotomous noise is described. The stochastic differential equation governing the flow implies smooth trajectories between noise switchingExpand
Resonances of chaotic dynamical systems.
  • Ruelle
  • Physics, Medicine
  • Physical review letters
  • 1986
TLDR
It appears desirable to analyze the decay of correlation functions and the possible analyticity of power spectra for physical time evolutions, and for computer generated simple dynamical systems (non-Axiom-A in general). Expand
Scaling behavior of the maximum energy exchange between coupled anharmonic oscillators.
TLDR
The maximum energy exchange of two harmonically coupled nonlinear oscillators is investigated and it is shown that the corresponding resonance curves have a universal shape and become broader and smaller when the amplitude-frequency coupling becomes large. Expand
Consolidated expansions for estimating the response of a randomly driven nonlinear oscillator
We consider a nonlinear oscillator driven by random, Gaussian “noise.” The oscillator, which is damped and has linear and cubic terms in the restoring force, is often called the “Duffing Equation.”Expand
Anharmonic Oscillator Driven by Additive Ornstein–Uhlenbeck Noise
We present an analytical study of a nonlinear oscillator subject to an additive Ornstein–Uhlenbeck noise. Known results are mainly perturbative and are restricted to the large dissipation limitExpand
Nonlinear resonances and suppression of chaos in the rf-biased Josephson junction.
TLDR
It is shown that aperiodic driving forces of very small amplitude can transform the junction from a stationary state into the rotation state and it can be shown that the resulting dynamics is not chaotic, in contrast to the generic dynamics resulting from a sinusoidal driving force. Expand
Optimal stimulation of a conservative nonlinear oscillator: Classical and quantum-mechanical calculations.
TLDR
A new method for nonlinear polychromatic resonant stimulation of conservative nonlinear oscillators is introduced, which considers a Morse potential that serves as a model for the HF molecule and shows that a large energy transfer is possible under optimal stimulation with small driving fields. Expand
Experimental evidence for mixed reality states in an interreality system.
TLDR
Experimental evidence is presented that, if the physical parameters of the simplified virtual system match those of the real system within a certain tolerance, there is a transition from an uncorrelated dual reality state to a mixed reality state of the system in which the motion of the two pendula is highly correlated. Expand
...
1
2
...