Related Experiment Video
Updated: Sep 9, 2025
06:31
Reconstitution of Cell-cycle Oscillations in Microemulsions of Cell-free Xenopus Egg Extracts
Published on: September 27, 2018
8.3K
Low-dimensional Watanabe-Strogatz approach for Kuramoto oscillators with higher-order interactions
1Complex Systems Lab, Department of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, India.
Chaos (Woodbury, N.Y.)
|September 4, 2025
Summary
Watanabe-Strogatz theory unifies descriptions of Kuramoto oscillator models with various interactions. Its parameters mirror mean-field dynamics, with Möbius transformation poles defining synchronization basin boundaries.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Theoretical Physics
Background:
- The Kuramoto model describes coupled oscillator synchronization.
- Watanabe-Strogatz theory simplifies Kuramoto oscillator dynamics using Möbius transformations.
- Existing theories often focus on pairwise interactions.
Purpose of the Study:
- To extend Watanabe-Strogatz theory for a broader class of Kuramoto oscillator models.
- To unify descriptions of models with pairwise and higher-order interactions.
- To analyze the role of Möbius transformation poles in synchronization dynamics.
Main Methods:
- Application of Watanabe-Strogatz theory to generalized Kuramoto models.
- Analysis of Möbius transformation properties and their relation to oscillator dynamics.
- Numerical simulations of synchronization phenomena and basin boundary evolution.
Main Results:
- A unified description for diverse Kuramoto oscillator models was achieved.
- Identical dynamics were found between Watanabe-Strogatz and mean-field parameters.
- Möbius transformation poles were identified as crucial for global and cluster synchronization basin boundaries.
Conclusions:
- Watanabe-Strogatz theory offers a powerful framework for analyzing complex oscillator networks.
- The identified basin boundaries provide insights into synchronization transitions.
- This work advances the understanding of synchronization in systems with complex interaction structures.
Related Concept Videos
01:07Damped Oscillations
6.0K
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...
6.0K
01:04Oscillations about an Equilibrium Position
5.6K
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...
5.6K
01:18Second Order systems II
169
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
169
01:06Forced Oscillations
6.8K
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.
6.8K
01:17Design Example: Underdamped Parallel RLC Circuit
376
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...
Starting with a fixed...
376
01:30Oscillations In An LC Circuit
2.5K
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
2.5K