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Oscillations In An LC Circuit01:30

Oscillations In An LC Circuit

An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by
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Fabrication and Testing of Microfluidic Optomechanical Oscillators
09:10

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Published on: May 29, 2014

Intermittent switching for three repulsively coupled oscillators.

Kentaro Ito1, Yasumasa Nishiura

  • 1Department of Mathematics, Graduate School of Science, Hokkaido University, Sapporo, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 4, 2008
PubMed
Summary
This summary is machine-generated.

Intermittent switching behaviors in three coupled oscillators were studied. Two routes to chaos with S3 symmetry were identified, one via Pomeau-Manneville intermittency and another through period doubling and crises.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems

Background:

  • Oscillatory systems exhibit complex behaviors, including intermittent switching.
  • Understanding the bifurcation scenarios leading to chaos is crucial in nonlinear dynamics.

Purpose of the Study:

  • To clarify the bifurcation scenario generating intermittent switching behaviors in a system of three identical, diffusively and repulsively coupled oscillators.
  • To investigate two distinct routes to chaos with S3 symmetry.

Main Methods:

  • Utilized the Stuart-Landau oscillator model, a general form of Hopf bifurcation.
  • Performed a numerical study of the bifurcation structure.

Main Results:

  • Identified two routes to chaos with S3 symmetry.
  • The inactive case exhibited Pomeau-Manneville intermittency, with trajectories switching among three symmetric tori.
  • The limit cycle case showed chaos with lower symmetry via period doubling, followed by S3 symmetric chaos after two attractor-merging crises.

Conclusions:

  • The study clarifies distinct bifurcation pathways to chaos in coupled oscillator systems.
  • Symmetry plays a critical role in the observed intermittent switching and chaotic dynamics.