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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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A relaxation oscillator is one of the applications of RC circuits. A neon lamp relaxation oscillator comprises a capacitor, a resistor, a voltage source, and a lamp. The lamp acts like an open circuit, with infinite resistance until the potential difference across the lamp reaches a specific voltage. At that voltage, the lamp acts like a short circuit with zero resistance, and the capacitor discharges through the lamp, thus producing light. Once the capacitor is fully discharged through the...
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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Pulse coupled oscillators and the phase resetting curve.

Carmen C Canavier1, Srisairam Achuthan

  • 1Neuroscience Center of Excellence, LSU Health Sciences Center, New Orleans, LA 70112, USA.

Mathematical Biosciences
|May 13, 2010
PubMed
Summary

Pulse coupled oscillators interact via brief pulses. Phase resetting curves (PRCs) predict phase locking in these networks, offering a robust method for analyzing complex oscillatory systems.

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Area of Science:

  • Computational Neuroscience
  • Nonlinear Dynamics
  • Systems Biology

Background:

  • Pulse coupled oscillators (PCOs) are systems where interactions occur through brief, discrete pulses.
  • The effect of one pulse diminishes before the next arrives, characteristic of many biological and physical systems.
  • Phase resetting curves (PRCs) quantify the impact of external stimuli on the timing of oscillations.

Purpose of the Study:

  • To explore a general approach for analyzing networks of pulse coupled oscillators using phase resetting curves.
  • To investigate methods for predicting and analyzing phase locking phenomena in PCOs.
  • To provide a framework for understanding oscillatory network dynamics beyond specific interaction forms.

Main Methods:

  • Formulating PCO analysis using a PRC derived from approximate biological network inputs.
  • Constructing discrete event-to-event maps based on circuit architecture and assumed firing patterns.
  • Analyzing fixed points of these maps to identify and assess the stability of periodic firing modes.
  • Developing PRC-based maps that do not require pre-supposed firing orders.

Main Results:

  • The use of PRCs allows for the prediction of phase locking in PCO networks.
  • Discrete maps derived from PRCs simplify the analysis of periodic firing modes compared to direct network analysis.
  • This general approach accommodates various network architectures, including unidirectionally coupled rings and all-to-all networks.
  • The framework is applicable to specific systems like periodically forced oscillators and bidirectionally coupled oscillators.

Conclusions:

  • Phase resetting curves provide a powerful and general tool for analyzing pulse coupled oscillator networks.
  • The discrete map approach simplifies the stability analysis of complex oscillatory dynamics.
  • This methodology offers a versatile framework applicable to diverse network configurations and coupling schemes in neuroscience and beyond.