Related Experiment Video
Updated: Jul 16, 2026
09:23
Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
Self-organized quasiperiodicity in oscillator ensembles with global nonlinear coupling
Michael Rosenblum1, Arkady Pikovsky
1Department of Physics, University of Potsdam, Am Neuen Palais 10, D-14469 Potsdam, Germany.
Physical Review Letters
|March 16, 2007
Summary
Researchers observed a shift from perfect synchronization to partial synchronization in coupled oscillators. An analytical model explains how the mean field can exhibit a different frequency, leading to complex quasiperiodic dynamics.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Theoretical Physics
Background:
- Ensembles of coupled oscillators often exhibit synchronized behavior.
- Understanding transitions between different synchronization states is crucial for complex systems.
- Nonlinear coupling introduces complex dynamics not seen in linear systems.
Purpose of the Study:
- To describe the transition from fully synchronous periodic oscillations to partially synchronous quasiperiodic dynamics.
- To introduce and analyze an analytically solvable model for this transition.
- To illustrate the phenomenon using specific physical systems.
Main Methods:
- Development of an analytically solvable model for coupled oscillators.
- Analysis of nonlinear, all-to-all coupling dependent on generalized order parameters.
- Numerical and analytical investigation of Landau-Stuart oscillators and Josephson junction arrays.
Main Results:
- A novel regime was identified where the mean field's frequency is incommensurate with individual oscillators.
- The mean field does not entrain individual oscillators in this regime.
- Self-organized onset of quasiperiodic dynamics was demonstrated.
Conclusions:
- Nonlinear coupling in oscillator ensembles can lead to complex quasiperiodic dynamics.
- The developed analytical model accurately predicts this transition.
- The findings are relevant for understanding synchronization phenomena in physical systems like Josephson junction arrays.
Related Concept Videos
01:04Oscillations 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...
01:31Oscillations 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
01:06Forced 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.
01:07Damped 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...
Although friction and other non-conservative...
01:30RLC 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...
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...
01:12Fermi Level Dynamics
The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...