# Resonant forcing of multidimensional chaotic map dynamics.

@article{Foster2007ResonantFO, title={Resonant forcing of multidimensional chaotic map dynamics.}, author={Glenn C. Foster and Alfred W. H{\"u}bler and Karin A. Dahmen}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2007}, volume={75 3 Pt 2}, pages={ 036212 } }

We study resonances of chaotic map dynamics. We use the calculus of variations to determine the additive forcing function that induces the largest response. We find that resonant forcing functions complement the separation of nearby trajectories, in that the product of the displacement of nearby trajectories and the resonant forcing is a conserved quantity. As a consequence, the resonant function will have the same periodicity as the displacement dynamics, and if the displacement dynamics is… Expand

#### 9 Citations

Resonant Forcing of Chaotic Dynamics

- Mathematics
- 2008

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… Expand

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

- Physics
- 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… Expand

Resonance Curves of Multidimensional Chaotic Systems

- Physics
- 2009

We study resonance curves of nonlinear dynamical systems with chaotic forcing functions. We use the calculus of variations to determine the forcing function that induces the largest response. We… Expand

Resonant forcing of nonlinear systems of differential equations.

- Mathematics, Physics
- Chaos
- 2008

We study resonances of nonlinear systems of differential equations, including but not limited to the equations of motion of a particle moving in a potential. We use the calculus of variations to… Expand

Reducing Microwave Absorption with Chaotic Microwaves

- Physics
- 2016

We study the response of a two-level quantum system to a chaotic signal using numerical methods and compare it to the response to a sinusoidal signal. We expect the largest response for sinusoidal… Expand

"Homeopathic" dynamical systems

- Computer Science
- Complex.
- 2008

Homeopathy contends that higher dilutions of the active ingredient in a remedy (fewer molecules in each dose) produce stronger medical effects [1]. This idea is inconsistent with observed… Expand

“Homeopathic” dynamical systems

- Physics
- 2008

Homeopathy contends that higher dilutions of the active ingredient in a remedy (fewer molecules in each dose) produce stronger medical effects [1]. This idea is inconsistent with observed… Expand

20. The Policy Conundrum of Financial Market Complexity

- 2011

The first global financial sector crash eludes conventional assessments of sector risk. Singling out the usual culprits – the housing bubble, executive pay, regulators, rating agencies, risk models,… Expand

The Policy Conundrum of Financial Market Complexity

- Business
- 2011

The first global financial sector crash eludes conventional assessments of sector risk. Singling out the usual culprits – the housing bubble, executive pay, regulators, rating agencies, risk models,… Expand

#### References

SHOWING 1-10 OF 15 REFERENCES

Resonances of nonlinear oscillators.

- Physics, Medicine
- Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1995

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

Resonances of chaotic dynamical systems.

- Physics, Medicine
- Physical review letters
- 1986

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

Zero-dispersion phenomena in oscillatory systems

- Physics
- 2003

Phenomena occurring in a particular class of nonlinear oscillatory systems—zero-dispersion systems—are reviewed for cases with and without damping while the system is driven either by random… Expand

Scaling behavior of the maximum energy exchange between coupled anharmonic oscillators.

- Physics, Medicine
- Physical review. A, Atomic, molecular, and optical physics
- 1990

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

Divergence of the chaotic layer width and strong acceleration of the spatial chaotic transport in periodic systems driven by an adiabatic ac force.

- Physics, Medicine
- Physical review letters
- 2005

We show for the first time that a weak perturbation in a Hamiltonian system may lead to an arbitrarily wide chaotic layer and fast chaotic transport. This generic effect occurs in any spatially… Expand

Nonlinear Oscillations Dynamical Systems, and Bifurcations of Vector Fields

- Mathematics, Physics
- 1983

Contents: Introduction: Differential Equations and Dynamical Systems.- An Introduction to Chaos: Four Examples.- Local Bifurcations.- Averaging and Perturbation from a Geometric Viewpoint.-… Expand

Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance

- Physics, Medicine
- Nature
- 2005

Stochastic resonance in nanomechanical systems could have a function in the realization of controllable high-speed nanomechamical memory cells, and paves the way for exploring macroscopic quantum coherence and tunnelling. Expand

Nonlinear resonances and suppression of chaos in the rf-biased Josephson junction.

- Physics, Medicine
- Physical review letters
- 1990

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.

- Physics, Medicine
- Physical review letters
- 1992

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

Direct observation of dynamical bifurcation between two driven oscillation states of a Josephson junction.

- Physics, Medicine
- Physical review letters
- 2005

A novel phase-sensitive microwave reflection experiment which directly probes the dynamics of the Josephson plasma resonance in both the linear and the nonlinear regime, and observes for the first time the transition between two different dynamical states predicted for nonlinear systems. Expand