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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Dynamics of coupled D-dimensional Stuart-Landau oscillators.

Pragjyotish Bhuyan Gogoi¹, Awadhesh Prasad¹, Aryan Patel²

¹University of Delhi, Department of Physics and Astrophysics, Delhi 110007, India.

Physical Review. E

|December 23, 2025

Summary

Researchers explored higher-dimensional Stuart-Landau oscillators, revealing new synchronization and oscillation death phenomena. These emergent dynamics in D>2 dimensions differ from the 2D case, offering novel insights into complex systems.

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Area of Science:

Nonlinear Dynamics
Complex Systems
Mathematical Physics

Background:

The Stuart-Landau oscillator is a fundamental model for studying oscillations.
Generalizations to higher dimensions (D>2) introduce SO(D) rotational symmetry.
Previous studies primarily focused on the D=2 case.

Purpose of the Study:

Investigate collective dynamics of K Stuart-Landau oscillators in D=3 and D=4 dimensions.
Analyze emergent phenomena when rotational symmetry is preserved or broken by coupling.
Explore the impact of heterogeneity on oscillator behavior.

Main Methods:

Studied systems of K Stuart-Landau oscillators in D=3 and D=4.
Varied coupling to either preserve or break SO(D) rotational symmetry.
Analyzed emergent phenomena including synchronization, multistability, and partial amplitude/oscillation death.

Main Results:

Preserving rotational symmetry leads to synchronization, multistability, and partial amplitude death (subset of variables quench to same value).
Broken rotational symmetry results in partial synchronization and partial oscillation death (subset of variables quench to different values).
Observed phase locking and phase drift in oscillatory dynamics.

Conclusions:

Higher-dimensional Stuart-Landau oscillators exhibit novel collective dynamics absent in 2D systems.
Coupling strategy (symmetry preserving vs. breaking) dictates the type of emergent phenomena.
The study expands understanding of synchronization and quenching in complex oscillatory systems.