Related Experiment Video
Updated: Jul 16, 2025
08:08
Oscillation and Reaction Board Techniques for Estimating Inertial Properties of a Below-knee Prosthesis
Published on: May 8, 2014
16.8K
Higher-order interactions in Kuramoto oscillators with inertia
Patrycja Jaros1, Subrata Ghosh1,2, Dawid Dudkowski1
1Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland.
Physical Review. E
|September 19, 2023
Summary
Higher-order interactions in coupled phase oscillators reveal new collective states beyond pairwise coupling. Adjusting phase lag and interaction sign is crucial for emergent network dynamics.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Network Science
Background:
- The dynamics of coupled oscillators are fundamental to many natural and engineered systems.
- Pairwise interactions are well-studied, but higher-order interactions can lead to novel emergent behaviors.
- Understanding these higher-order effects is key to fully characterizing complex network dynamics.
Purpose of the Study:
- To investigate the influence of higher-order interactions on the dynamical landscape of coupled phase oscillators.
- To identify new collective states emerging from higher-order coupling that are absent in pairwise interaction models.
- To explore the parameter space encompassing phase lag and coupling strength for both pairwise and higher-order interactions.
Main Methods:
- Utilized a network model of three coupled Kuramoto phase oscillators with inertia.
- Systematically varied phase lag and coupling strength (both pairwise and higher-order) across a broad range.
- Employed numerical simulations to identify and classify various collective states within the extended parameter space.
Main Results:
- Observed known states like synchronization, frequency chimera states, and rotating waves with distinct parameter boundaries.
- Discovered novel states, specifically the 2+1 antipodal point and 2+1 phase-locked states, driven by higher-order interactions.
- Demonstrated the critical importance of phase lag and the sign of higher-order coupling strength on emergent dynamics.
Conclusions:
- Higher-order interactions significantly expand the repertoire of collective states in oscillator networks.
- The interplay between phase lag and the nature of higher-order coupling dictates complex network behavior.
- Analytical support validates the numerical findings, highlighting the role of higher-order effects in oscillator dynamics.
Related Concept Videos
01:06Forced Oscillations
6.6K
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.
6.6K
01:04Oscillations about an Equilibrium Position
5.4K
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...
5.4K
01:07Damped Oscillations
5.8K
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...
5.8K
01:17Second-Order Circuits
1.4K
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...
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...
1.4K
01:18Second Order systems II
130
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.
130
01:20Types of Damping
6.5K
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...
6.5K