Long-period clocks from short-period oscillators

Area of Science:

• Complex systems
• Nonlinear dynamics
• Statistical physics

Background:

• Kuramoto oscillators are fundamental models for synchronization in coupled systems.
• Disorder in natural frequencies is a common feature in real-world oscillatory systems.
• Understanding emergent macroscopic behavior from microscopic interactions is a key challenge.

Purpose of the Study:

• To investigate the dynamics of repulsively coupled Kuramoto oscillators with a distribution of natural frequencies.
• To identify emergent macroscopic time scales and patterns of phase-locked motion.
• To explore the role of frequency distribution width in shaping system dynamics.

Main Methods:

• Analysis of repulsively coupled Kuramoto oscillator networks.
• Mathematical modeling of systems with a distribution of natural frequencies.
• Characterization of phase-locked states and their temporal patterns.

Main Results:

• Disorder in natural frequencies leads to macroscopic clocks with repetitive, temporary phase-locked motion.
• Emergent periods can be significantly longer than individual oscillator periods.
• Self-similar sequences of phase-locked motion across different time scales were observed, with ratios determined by frequency distribution widths.

Conclusions:

• Repulsively coupled Kuramoto oscillators with frequency disorder can generate complex dynamics and macroscopic clocks.
• The width of the natural frequency distribution is a critical parameter controlling emergent time scales.
• These systems exhibit intrinsic flexibility in dynamics and temporal patterns without external forcing.