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Related Concept Videos

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
RLC Circuit as a Damped Oscillator01:30

RLC Circuit as a Damped Oscillator

An RLC circuit combines a resistor, inductor, and capacitor, connected in a series or parallel combination.
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
Design Example: Underdamped Parallel RLC Circuit01:17

Design Example: Underdamped Parallel RLC Circuit

Consider designing an oscillator circuit, a crucial component in various electronic devices and systems. The objective is to create an oscillator circuit with specific characteristics: a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. To accomplish this, a parallel RLC circuit is employed, known for its ability to sustain oscillations at a resonant frequency. In this case, the damping factor is pivotal in achieving the desired performance.
Starting with a fixed...
Current Growth And Decay In RL Circuits01:30

Current Growth And Decay In RL Circuits

The current growth and decay in RL circuits can be understood by considering a series RL circuit consisting of a resistor, an inductor, a constant source of emf, and two switches. When the first switch is closed, the circuit is equivalent to a single-loop circuit consisting of a resistor and an inductor connected to a source of emf. In this case, the source of emf produces a current in the circuit. If there were no self-inductance in the circuit, the current would rise immediately to a steady...
Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next sampling...
Second-Order Circuits01:17

Second-Order Circuits

Integrating two fundamental energy storage elements in electrical circuits results in second-order circuits, encompassing RLC circuits and circuits with dual capacitors or inductors (RC and RL circuits). Second-order circuits are identified by second-order differential equations that link input and output signals.
Input signals typically originate from voltage or current sources, with the output often representing voltage across the capacitor and/or current through the inductor. For example, in...

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Reconstitution of Cell-cycle Oscillations in Microemulsions of Cell-free Xenopus Egg Extracts
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Published on: September 27, 2018

Reconstructing phase dynamics of oscillator networks.

Björn Kralemann1, Arkady Pikovsky, Michael Rosenblum

  • 1Institut für Pädagogik, Christian-Albrechts-Universität zu Kiel, Olshausenstr. 75, 24118 Kiel, Germany.

Chaos (Woodbury, N.Y.)
|July 5, 2011
PubMed
Summary

This study reconstructs phase dynamics and coupling functions for small networks of coupled oscillators using time series data. The method quantifies directed coupling and reveals nonlinear coupling effects.

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Area of Science:

  • Nonlinear dynamics
  • Network science
  • Time series analysis

Background:

  • Coupled oscillator systems are fundamental in various scientific fields.
  • Reconstructing phase dynamics from observational data is crucial for understanding system behavior.
  • Existing methods may be limited in applicability to small network structures.

Purpose of the Study:

  • To generalize a phase dynamics reconstruction method for coupled oscillators.
  • To analyze small networks of coupled periodic units.
  • To quantify directed coupling and explore nonlinear effects.

Main Methods:

  • Generalizing a prior approach for phase dynamics reconstruction.
  • Utilizing multivariate time series data as input.
  • Reconstructing genuine phases and coupling functions.
  • Quantifying directed coupling via partial norms of coupling functions.

Main Results:

  • Successfully reconstructed phase dynamics and coupling functions for small networks.
  • Illustrated the method with various network motifs (3, 5, and 9 units).
  • Demonstrated the quantification of directed coupling between oscillators.
  • Provided insights into nonlinear coupling effects within these systems.

Conclusions:

  • The generalized method effectively analyzes phase dynamics in small coupled oscillator networks.
  • The approach allows for the quantification of directed interactions.
  • The study highlights the importance of considering nonlinear coupling effects.