Coarse graining the dynamics of coupled oscillators

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Computational Physics

Background:

• Coupled oscillator systems are fundamental in various scientific domains.
• Understanding synchronization dynamics in finite, nonidentical assemblies presents significant challenges.
• Existing methods often require complex mathematical derivations for long-term predictions.

Purpose of the Study:

• To present an equation-free computational approach for studying coarse-grained dynamics.
• To analyze the synchronization behavior of finite assemblies of nonidentical coupled oscillators.
• To overcome limitations of traditional methods in predicting long-term dynamics.

Main Methods:

• Utilizing coarse-grained observables that capture correlations between phase angles and natural frequencies.
• Employing short bursts of initialized detailed simulations.
• Circumventing the need for closure derivations in analyzing assembly statistics.

Main Results:

• Successfully studied the coarse-grained dynamics of nonidentical coupled oscillators near full synchronization.
• Demonstrated an efficient method for analyzing complex oscillator assemblies.
• Provided insights into the dynamics without relying on lengthy mathematical derivations.

Conclusions:

• The equation-free approach offers an efficient alternative for studying complex oscillator systems.
• This method facilitates the analysis of synchronization phenomena in finite assemblies.
• The approach is particularly useful for systems where deriving closed-form dynamics is intractable.