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Related Concept Videos

Forced Oscillations01:06

Forced Oscillations

When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.
Damped Oscillations01:07

Damped Oscillations

In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
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Properties of Laplace Transform-II01:16

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Types of Damping01:20

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If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...
Second Order systems II01:18

Second Order systems II

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If  ζ...

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Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
11:21

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

Periodicity suppression in continuous-time dynamical systems by external forcing.

Amanda C Mathias1, Paulo C Rech

  • 1Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710 Joinville, Brazil. amaandafisica@gmail.com

Chaos (Woodbury, N.Y.)
|January 3, 2013
PubMed
Summary
This summary is machine-generated.

External periodic forcing can suppress periodicity in chaotic systems. Numerical simulations demonstrate that even embedded periodic windows can be entirely eliminated by adjusting forcing amplitude.

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Area of Science:

  • Nonlinear dynamics
  • Fluid mechanics
  • Chaos theory

Background:

  • Autonomous nonlinear systems often exhibit complex dynamics, including chaos.
  • External periodic forcing is a common method to influence system behavior.
  • Understanding the interplay between intrinsic dynamics and external perturbations is crucial.

Purpose of the Study:

  • To investigate the suppression of periodicity in nonlinear systems subjected to external periodic forcing.
  • To determine the conditions under which periodic behaviors embedded within chaotic attractors can be eliminated.
  • To analyze the impact of forcing amplitude on periodicity suppression.

Main Methods:

  • Modeling fluid flows using sets of three autonomous nonlinear first-order ordinary differential equations.
  • Performing numerical simulations to explore system dynamics.
  • Utilizing parameter plane plots, phase-space portraits, and largest Lyapunov exponent calculations to characterize system behavior.

Main Results:

  • Demonstrated that external periodic forcing can lead to the complete suppression of periodicity.
  • Identified that windows of periodicity embedded within chaotic regions are susceptible to suppression.
  • Showed that varying the amplitude of sinusoidal forcing significantly affects the presence of periodic behavior.

Conclusions:

  • External periodic forcing is an effective tool for suppressing inherent periodicity in nonlinear systems.
  • The amplitude of the applied forcing is a critical parameter in determining the extent of periodicity suppression.
  • These findings have implications for controlling chaotic behavior in various physical systems.