Related Experiment Video
Updated: Apr 27, 2026
08:02
Generation of Local CA1 γ Oscillations by Tetanic Stimulation
Published on: August 14, 2015
8.5K
Synchronization of oscillators in a Kuramoto-type model with generic coupling
Vladimir Vlasov1, Elbert E N Macau2, Arkady Pikovsky1
1Department of Physics and Astronomy, Potsdam University, 14476 Potsdam, Germany.
Chaos (Woodbury, N.Y.)
|July 3, 2014
Summary
We present a generalized Kuramoto-Sakaguchi model for coupled oscillators. Our solutions offer new insights into synchronization dynamics, applicable to both noise-free and noisy systems.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Network Science
Background:
- Coupled oscillator systems are fundamental in understanding emergent phenomena.
- The Kuramoto-Sakaguchi model is a standard but limited framework.
- Generalizing mean-field coupling is crucial for realistic network dynamics.
Purpose of the Study:
- To develop and solve a generalized mean-field coupling model for oscillators.
- To provide explicit parametric solutions for mean-field amplitude and frequency.
- To analyze synchronization properties in networks with heterogeneous oscillator contributions.
Main Methods:
- Development of a generalized mean-field coupling framework.
- Derivation of self-consistency equations for mean-field properties.
- Parametric solution of these equations for noise-free and noise-driven cases.
- Application to spatially extended oscillators with finite signal velocity.
Main Results:
- Explicit parametric solutions for mean-field amplitude and frequency were obtained.
- The generalized model accommodates varying oscillator contributions and mean-field interactions.
- Solutions are valid for both deterministic and stochastic oscillator dynamics.
- Analysis of spatially spread oscillators demonstrates the model's applicability.
Conclusions:
- The generalized model provides a powerful tool for studying complex oscillator networks.
- The derived solutions simplify the analysis of synchronization phenomena.
- This work extends the applicability of mean-field theory to more diverse network structures.
Related Concept Videos
01:04Oscillations about an Equilibrium Position
5.7K
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...
5.7K
01:07Damped Oscillations
6.2K
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...
6.2K
01:06Forced Oscillations
6.3K
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.
6.3K
01:30Oscillations In An LC Circuit
2.6K
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
2.6K
01:30RLC Circuit as a Damped Oscillator
2.7K
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...
2.7K
01:17Design Example: Underdamped Parallel RLC Circuit
816
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...
816