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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
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.
Although friction and other non-conservative...
Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so because...
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.
Transient and Steady-state Response01:24

Transient and Steady-state Response

In control systems, test signals are essential for evaluating performance under various conditions. The ramp function is effective for systems undergoing gradual changes, while the step function is suitable for assessing systems facing sudden disturbances. For systems subjected to shock inputs, the impulse function is the most appropriate test signal.
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state response.
Types of Damping01:20

Types of Damping

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...

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Related Experiment Video

Updated: May 24, 2026

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice
07:33

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice

Published on: June 29, 2018

Transitory behaviors in diffusively coupled nonlinear oscillators.

Satoru Tadokoro, Yutaka Yamaguti, Hiroshi Fujii

    Cognitive Neurodynamics
    |March 2, 2012
    PubMed
    Summary
    This summary is machine-generated.

    Collective behaviors in diffusively coupled oscillators show intermittent dynamics, including synchronized states and metachronal waves. These patterns emerge regardless of oscillator number, driven by coupling strength and dephasing interactions.

    Keywords:
    Diffusively coupled systems of oscillatorsIn-out intermittencyMetachronal wavesOut-of-phase synchrony

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    An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

    Published on: December 4, 2017

    Area of Science:

    • Physics
    • Nonlinear Dynamics
    • Complex Systems

    Background:

    • Diffusively coupled oscillators are fundamental models for studying synchronization phenomena.
    • Out-of-phase synchrony is a key behavior observed in coupled oscillator systems.
    • Understanding collective behaviors in large populations is crucial for various scientific fields.

    Purpose of the Study:

    • To investigate the diverse collective behaviors of diffusively coupled oscillators with nearest-neighbor interactions.
    • To analyze the intermittent dynamics, including synchronized states, chaotic states, and metachronal waves.
    • To interpret the observed intermittent behavior as in-out intermittency.

    Main Methods:

    • Analysis of weakly interacting two-oscillator systems to understand fundamental dephasing interactions.
    • Simulation and theoretical analysis of large populations of one-dimensionally coupled oscillators.
    • Identification of invariant subspaces and saddle points to explain intermittent dynamics.

    Main Results:

    • Various collective behaviors emerge in large oscillator populations, dependent on coupling strength, not population size.
    • Intermittent behavior is observed, characterized by transitions between all-synchronized states, weakly chaotic states, and metachronal waves.
    • Metachronal waves, featuring orderly phase shifts, are generated by dephasing interactions.

    Conclusions:

    • The study reveals complex collective dynamics in coupled oscillator systems, highlighting the role of coupling strength.
    • The observed intermittent behavior can be explained through the concept of in-out intermittency, involving specific saddle states.
    • The findings contribute to the understanding of emergent patterns in complex systems and nonlinear dynamics.