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
Expected Dynamics
Oscillators drift independently, no synchronization
Gradual emergence of partial synchronization
Rapid convergence to full synchronization
Live Oscillator Dynamics
Phase Space Analysis
Ready to Explore Synchronization
Configure parameters and click "Run Simulation" to visualize oscillator dynamics