Oscillator Synchronization

Real-time visualization of coupled oscillator dynamics and collective synchronization

What is This?

Collective Synchronization

This interactive tool demonstrates how independent oscillators spontaneously synchronize through coupling. Watch as chaotic, desynchronized oscillators gradually align their phases, converging to a unified rhythm—a phenomenon observed everywhere from firefly flashing to neuronal firing.

Two Models

  • Kuramoto Model: Continuous phase coupling where oscillators adjust based on phase differences
  • Firefly Model: Pulse-coupled synchronization mimicking firefly flash patterns

Key Concepts

  • Coherence (|ψ|): Measures synchronization strength (0 = chaotic, 1 = perfect sync)
  • Phase Space: Circular plot showing oscillator positions on unit circle
  • Mean Field: Red arrow showing collective phase direction
  • Coupling Strength (K): How strongly oscillators influence each other

Spectral Law Connection

This simulation uses the same spectral phase dynamics principles that power the prime kernel and other coherence-based tests. Phase alignment emerges through the same energy balance framework underlying prime detection and pattern convergence.

Live Visualization

The wave plot shows overlaid oscillations converging to the red mean field. The phase space shows oscillators clustering around the mean direction as they synchronize.

Simulation Parameters

Continuous phase synchronization via phase differences

2200
0 (no coupling)5 (strong)
0 (synchronized)1 (random)
5s60s

Expected Dynamics

Weak Coupling (K < 1):

Oscillators drift independently, no synchronization

Critical Coupling (K ≈ 1-2):

Gradual emergence of partial synchronization

Strong Coupling (K > 2):

Rapid convergence to full synchronization

Live Oscillator Dynamics

Phase Space Analysis

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Ready to Explore Synchronization

Configure parameters and click "Run Simulation" to visualize oscillator dynamics

Tip: Start with K=1.5 for the Kuramoto model to see synchronization emerge