Related Experiment Video
Updated: Apr 5, 2026
06:31
Reconstitution of Cell-cycle Oscillations in Microemulsions of Cell-free Xenopus Egg Extracts
Published on: September 27, 2018
8.7K
Synchronization as Aggregation: Cluster Kinetics of Pulse-Coupled Oscillators.
Kevin P O'Keeffe1, P L Krapivsky2, Steven H Strogatz3
1Department of Physics, Cornell University, Ithaca, New York 14853, USA.
Physical Review Letters
|August 22, 2015
Summary
This study quantifies how small synchronized oscillator clusters merge into larger ones. We provide exact results for cluster size distribution during the transition from disorder to synchrony.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Statistical physics
Background:
- Identical pulse-coupled oscillators with global interactions often synchronize.
- Previous research established synchronization but lacked quantification of cluster coalescence.
- Understanding cluster dynamics is crucial for complex system behavior.
Purpose of the Study:
- To quantify the progressive merging of synchronized oscillator clusters.
- To derive exact results for the distribution of cluster sizes over time.
- To analyze the transition from disordered states to full synchrony.
Main Methods:
- Modeling identical pulse-coupled oscillators with global interactions.
- Applying tools from the mathematical study of aggregation phenomena.
- Deriving exact analytical results for time-dependent cluster size distributions.
Main Results:
- Obtained exact results for the time-dependent distribution of cluster sizes.
- Quantified the coalescence process of small synchronized clusters into larger ones.
- Characterized the evolution of the system from disorder to synchrony.
Conclusions:
- The study provides a precise mathematical framework for understanding oscillator cluster aggregation.
- Exact results offer new insights into the dynamics of complex systems transitioning to synchrony.
- Findings are applicable to various fields involving coupled oscillatory phenomena.
Related Concept Videos
01:30Oscillations In An LC Circuit
3.4K
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
3.4K
01:16Cascaded Op Amps
1.3K
Operational amplifiers (op-amps) are versatile electronic components that can be interconnected in a cascade - one after another in a linear sequence. This cascading is possible due to their infinite input resistance and zero output resistance, allowing them to maintain their input-output relationships even when connected in series.
In a cascaded system, each op-amp is referred to as a stage. The output of one stage drives the input of the subsequent stage. As the input signal passes through...
In a cascaded system, each op-amp is referred to as a stage. The output of one stage drives the input of the subsequent stage. As the input signal passes through...
1.3K
01:04Oscillations about an Equilibrium Position
7.3K
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...
7.3K
01:06Forced Oscillations
8.3K
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.
8.3K
01:07Damped Oscillations
7.6K
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...
7.6K
01:30RLC Circuit as a Damped Oscillator
2.6K
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...
2.6K