Related Experiment Video
Updated: Jan 27, 2026
07:02
Phase Contrast Magnetic Resonance Imaging in the Rat Common Carotid Artery
Published on: September 5, 2018
9.9K
Repulsively coupled Kuramoto-Sakaguchi phase oscillators ensemble subject to common noise
Chen Chris Gong1, Chunming Zheng1, Ralf Toenjes1
1Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Straße 32, 14476 Potsdam, Germany.
Chaos (Woodbury, N.Y.)
|April 1, 2019
Summary
Clustering in the Kuramoto-Sakaguchi model is a numerical artifact, not a real phenomenon. Real multicluster states can occur in other oscillator systems like Van der Pol oscillators.
Area of Science:
- Physics
- Nonlinear Dynamics
- Complex Systems
Background:
- The Kuramoto-Sakaguchi model describes coupled phase oscillators, often exhibiting multicluster states under repulsive coupling and common noise.
- Previous simulations suggested stable multicluster states in this regime, but their physical reality was questioned.
Purpose of the Study:
- To investigate the formation of multicluster states in the Kuramoto-Sakaguchi model.
- To differentiate between genuine multicluster states and numerical artifacts.
- To explore conditions for multicluster formation in other oscillator systems.
Main Methods:
- Analysis of the Kuramoto-Sakaguchi model using Watanabe-Strogatz theory.
- Numerical integration with varying time steps to identify artifacts.
- Quantification of numerical errors using integrals of motion.
- Analysis of the Fokker-Planck equation to determine state attractivity.
Main Results:
- Identical phase oscillators in the Kuramoto-Sakaguchi model cannot form stable clusters due to system integrability.
- Observed clustering is a numerical artifact stemming from integration errors.
- Two-cluster states are non-attractive in this model.
- Multicluster states naturally occur in anharmonic oscillators like Van der Pol oscillators.
Conclusions:
- The formation of multicluster states in the Kuramoto-Sakaguchi model is an artifact of numerical integration.
- The integrability of the system prevents genuine cluster formation.
- Multicluster states are possible in more general oscillator systems with anharmonicity and amplitude dynamics.
Related Concept Videos
03:24Common Ion Effect
46.2K
Compared with pure water, the solubility of an ionic compound is less in aqueous solutions containing a common ion (one also produced by dissolution of the ionic compound). This is an example of a phenomenon known as the common ion effect, which is a consequence of the law of mass action that may be explained using Le Châtelier’s principle. Consider the dissolution of silver iodide:
46.2K
01:30Oscillations In An LC Circuit
3.1K
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
3.1K
01:06Forced Oscillations
7.7K
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.
7.7K
01:07Damped Oscillations
6.8K
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...
6.8K
01:04Oscillations about an Equilibrium Position
6.8K
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...
6.8K
02:33Phase Transitions: Sublimation and Deposition
19.9K
Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...
19.9K