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Two panels compare control strategies over a 2.0s closure window.
Left (Suppression, orange): irregular tangled trajectory in phase space, C̃=1.63, 17% energy efficiency, 19/116 closure ratio.
Right (PAC, green): compact directional orbit, C̃=0.78, 64% energy efficiency, 20/116 closure ratio.
Each panel shows a circular phase-space plot with trajectory and boundary points, a vertical histogram, and a θ(t) time series below.
Both receive identical noise (σ=0.50) and authority (2.20) - the difference is purely in control objective.
What This Demo Compares
Two identical noisy oscillators receive the same energy budget for control. The left panel uses suppression (damping) - it tries to reduce motion. The right panel uses phase-aligned control (PAC) - it biases the system toward closure without fighting the oscillation.
The contrast illustrates a core ResonanT⁴ insight: stability is not the same as stillness. Closure-compatible control can achieve structural coherence that suppression cannot.
Parameters
Playback
- Start / Pause / Reset
- Control the simulation playback.
- Control: ON/OFF
- Toggle whether control is applied. When OFF, both oscillators evolve under noise alone.
Presets
- Canonical (stable closure)
- Default parameters where PAC achieves clear closure advantage.
- Edge of closure
- Lower noise, higher authority - PAC barely maintains closure.
- Beyond closure
- High noise overwhelms both strategies - neither achieves closure.
Advanced
- Noise σ
- Standard deviation of the stochastic forcing applied to both oscillators.
- Authority
- Control gain - how strongly the controller can influence the system.
- Seed
- Random seed for reproducible noise sequences. Reseed to try different realizations.
- Show full trail
- Display the complete trajectory history instead of a sliding window.
- Convergence
- Show convergence metrics over time.
To understand the theory behind phase-aligned control:
Read Paper II