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Oscillations In An LC Circuit01:30

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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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Mixed-mode oscillation suppression states in coupled oscillators.

Debarati Ghosh1, Tanmoy Banerjee1

  • 1Department of Physics, University of Burdwan, Burdwan 713 104, West Bengal, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 15, 2015
PubMed
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Researchers discovered novel oscillation suppression states in coupled chaotic systems. These mixed-mode death (MMD) and mixed nontrivial asynchronous death (MNAD) states have potential applications in lasers and geomagnetic systems.

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Area of Science:

  • Nonlinear Dynamics
  • Complex Systems
  • Chaos Theory

Background:

  • Coupled oscillator systems exhibit diverse collective behaviors.
  • Oscillation suppression is a key phenomenon in nonlinear dynamics.
  • Understanding heterogeneous steady states is crucial for complex systems.

Purpose of the Study:

  • To identify and characterize novel collective dynamical states in coupled chaotic systems.
  • To investigate the mechanisms behind mixed-mode oscillation suppression.
  • To explore the occurrence and transitions of these states in parameter space.

Main Methods:

  • Analysis of the chaotic Lorenz system and Lorenz-like systems.
  • Bifurcation analysis to establish state occurrences.
  • Experimental validation of theoretical findings.

Main Results:

  • Identification of two mixed-mode oscillation suppression states: mixed-mode death (MMD) and mixed nontrivial asynchronous death (MNAD).
  • MMD involves heterogeneous and common steady states; MNAD involves simultaneous bistable and monostable states.
  • Symmetry breaking (reflection and translational) dictates the emergence of MMD and MNAD states.

Conclusions:

  • The study establishes the existence and transition routes of MMD and MNAD states.
  • Experimental results confirm the theoretical predictions.
  • Findings advance the understanding of oscillation suppression and may impact laser and geomagnetic systems.