Skip to content

Domain Utilisation Schemas

Cross-domain comparison of the current SPO domainpack catalogue, showing how Kuramoto/UPDE phase dynamics map to diverse physical, biological, and engineered systems.

The rows describe modelling intent and packaged configuration, not field validation. Safety Tier and Pipeline are binding metadata; labels such as clinical, production, consumer, and full do not certify a detector, controller, deployment, or regulatory status. See the Use Cases and Value Map for current evidence boundaries.

Master Domainpack Table

Pack Layers Osc Safety Tier Pipeline Key Innovation
agent_coordination 3 12 research full Multi-agent AI sync (heartbeat, task, topic)
autonomous_vehicles 3 8 research full Vehicle platoon phase-locking
bio_stub 4 16 research full Multi-scale biological oscillators
brain_connectome 4 12 research full HCP-inspired structural connectivity
cardiac_rhythm 4 10 clinical full Gap-junction coupling, arrhythmia
chemical_reactor 4 10 production full Hopf bifurcation, Semenov limit
circadian_biology 4 10 research full SCN clock-gene coupled oscillators
epidemic_sir 3 8 research full Epidemic wave synchronisation
financial_markets 4 8 research full Hilbert phase, crash regime detection
firefly_swarm 2 8 research full Mirollo-Strogatz flash synchronisation
fusion_equilibrium 6 12 research full MHD equilibrium + FusionCoreBridge
gene_oscillator 3 6 research full Repressilator + quorum sensing
geometry_walk 2 8 research full Random walk on graphs
identity_coherence 6 35 research full SSGF identity model, chimera + plasticity
laser_array 3 8 research full Evanescent-coupled laser phase-locking
manufacturing_spc 3 9 consumer full SPC process drift detection
metaphysics_demo 3 7 research full P/I/S + imprint + geometry
minimal_domain 2 4 research full Minimal-but-complete pipeline example
musical_acoustics 3 9 research full Consonance and groove via harmonic sync
network_security 3 8 research full DDoS detection via traffic sync anomaly
neuroscience_eeg 6 14 research full EEG band->phase, seizure detection
plasma_control 8 16 research adapter Full tokamak layer hierarchy (PlasmaControlBridge)
pll_clock 3 8 production full PLL network clock sync (ITU-T G.811)
power_grid 5 12 production full Swing equation = Kuramoto (exact)
power_safety_nchannel 3 6 production full Six-channel grid safety profile
quantum_simulation 3 8 research adapter Quantum gate phase tracking (QuantumControlBridge)
queuewaves 3 6 consumer full Service queue oscillations
robotic_cpg 4 8 consumer full Quadruped CPG locomotion gait patterns
rotating_machinery 4 10 consumer full Vibration harmonics, ISO 10816
satellite_constellation 3 8 research full Orbital slot + comms link sync
sleep_architecture 4 8 research full AASM sleep staging from R values
swarm_robotics 3 8 consumer full Vicsek collective motion/formation
traffic_flow 4 10 consumer full Signal coordination = phase sync
vortex_shedding 3 9 research full Wake dynamics (Stuart-Landau amplitude)
digital_twin_nchannel 3 6 production full Six-channel plant/twin residual profile
edge_consensus_nchannel 3 6 production full Six-channel gossip consensus with load/trust coupling

Pipeline types: full = BoundaryObserver + RegimeManager + SupervisorPolicy + PolicyEngine + ImprintModel (where applicable). adapter = uses a specialised bridge class (FusionCoreBridge, PlasmaControlBridge, QuantumControlBridge) as an alternative architecture.

Why Kuramoto Fits Each Domain

Neuroscience (EEG)

Neural populations oscillate at characteristic band frequencies. Bandpass filtering -> Hilbert transform yields instantaneous phase, which IS a Kuramoto oscillator phase. Inter-region phase-locking value (PLV) measures synchronisation. Buzsaki (2006) Rhythms of the Brain; Fries (2005) "Communication through Coherence".

Power Systems

The swing equation d delta/dt = omega is literally a second-order Kuramoto model. PMU phasor angles are oscillator phases; line admittances are coupling constants. No phase extraction step is needed -- measurement IS phase. Dorfler, Chertkov, Bullo (2013).

Cardiac Electrophysiology

Gap-junction (connexin-43) electrical coupling between cardiac cells is Kuramoto coupling with coupling constant proportional to gap junction conductance. SA node pacemaker cells entrain downstream tissue exactly as high-frequency Kuramoto oscillators entrain slower ones. Strogatz (2003) Sync.

Rotating Machinery

Vibration harmonics (1X, 2X, 3X) of shaft rotation, bearing defect frequencies (BPFI, BPFO, FTF), and structural resonance modes form a coupled oscillator network linked by mechanical impedance. Phase relationships between harmonics diagnose faults: 1X+2X in-phase signals misalignment. ISO 10816-3.

Chemical Reactors

CSTR systems undergo Hopf bifurcations where concentration and temperature oscillate with well-defined phase relationships. The Arrhenius-heat coupling creates limit cycles naturally modelled as coupled oscillators. Fogler (2020) Ch. 12.

Plasma Physics

Micro-turbulence, zonal flows, MHD tearing modes, sawteeth/ELMs, and transport barriers form a multi-timescale oscillator hierarchy. The predator-prey relationship between turbulence and zonal flows is a classic coupled-oscillator problem. ITER Physics Basis (2007).

Manufacturing SPC

Sensor signals (vibration, temperature, pressure) oscillate around setpoints. Tool wear causes systematic drift that correlates sensor phases -- exactly the kind of synchronisation Kuramoto detects.

Queue Networks

Service queues exhibit oscillatory behaviour under periodic demand. Phase relationships between upstream and downstream queues determine system throughput. Spiked arrivals synchronise queue oscillations.

Circadian Biology

SCN neurons are literal coupled oscillators with ~24 h period. Clock genes (Per/Cry, Bmal1, Rev-erb) form transcription-translation feedback loops whose phase relationships determine circadian entrainment. Winfree (1967); Strogatz (2003) Sync Ch. 5.

Traffic Flow

Traffic signal coordination IS phase synchronisation. Each signalised intersection cycles with period ~90 s; offset-based green wave coordination aligns phase differences between adjacent signals. Gershenson & Rosenblueth (2012) showed self-organising traffic lights converge via coupled-oscillator dynamics.

Epidemic SIR

Epidemic waves oscillate with well-defined periods driven by seasonal forcing, immunity waning, and intervention cycles. The SIR model produces damped oscillations that are naturally phase-coupled across regions via mobility. Seasonal forcing acts as external drive (zeta). Earn et al. (2000).

Biology (Bio Stub)

Biological systems oscillate at every scale: Ca2+ transients (ms), cardiac rhythm (s), circadian clocks (24 h), hormonal cycles (days-weeks). Multi-scale coupling between cellular, tissue, organ, and systemic layers is inherently a Kuramoto hierarchy.

Graph Geometry (Geometry Walk)

Random walkers on a graph synchronise when coupling exceeds a critical threshold related to spectral gap. Phase = ring-mapped node index (theta = 2pis/N). Clustering and fragmentation transitions map to Kuramoto order parameter bifurcations.

Minimal Domain

Minimal 2-layer, 4-oscillator test harness exercising every pipeline component: CouplingBuilder, UPDEEngine, BoundaryObserver, RegimeManager, SupervisorPolicy, PolicyEngine. Reference implementation for new domain authors.

Fusion Equilibrium

Grad-Shafranov equilibrium, MHD stability, transport, and ELM/sawtooth events form a coupled oscillator hierarchy. FusionCoreBridge maps tokamak observables (q-profile, beta_N, tau_E) to oscillator phases. ITER Physics Basis (2007).

Laser Arrays

Semiconductor laser arrays couple via evanescent fields in shared waveguide substrates. Each laser's optical phase evolves under gain competition and nearest-neighbour evanescent coupling — structurally identical to Kuramoto with finite-range coupling. Winful & Wang, Appl Phys Lett 53(20), 1988; Kozyreff et al., PRL 85(18), 2000.

PLL Clock Networks

Phase-locked loops track a reference clock by adjusting VCO frequency proportional to phase error — exactly the Kuramoto coupling term K·sin(θ_ref − θ_vco). Hierarchical PLL networks (stratum clocks) synchronise via cascaded phase detectors. Strogatz & Mirollo, SIAM J Appl Math 1988; ITU-T G.811.

Firefly Swarms

Firefly flash synchronisation is the canonical biological Kuramoto example. Each firefly adjusts its flash-phase based on visual coupling to neighbours, converging to collective synchrony. Mirollo & Strogatz (1990) proved global synchronisation for identical pulse-coupled oscillators.

Swarm Robotics

The Vicsek model — robots aligning heading angles with neighbours plus noise — is a discrete-time Kuramoto model on a proximity graph. Heading phase = oscillator phase; alignment = coupling. Vicsek et al., PRL 75(6), 1995; Cucker & Smale, IEEE TAC 2007.

Autonomous Vehicles

Vehicle platoons maintain fixed headway via adaptive cruise control. Each vehicle's position oscillates around the desired following distance — a phase-coupled system where synchronisation = stable platoon and desynchronisation = collision risk or string instability. Dey et al., IEEE Trans Intell Transp Syst 17(5), 2016.

Brain Connectome

HCP-derived structural connectivity matrices define coupling topology between cortical regions. Each region oscillates at characteristic frequencies; the connectome determines which regions phase-lock. Bullmore & Sporns, Nature Reviews Neuroscience 10, 2009.

Financial Markets

Asset returns exhibit collective synchronisation preceding crashes. Hilbert-transformed price series yield instantaneous phases; the Kuramoto order parameter R(t) → 1 signals herding behaviour. Harmon et al., PLoS ONE 6(4), 2011.

Gene Oscillator

The repressilator (Elowitz & Leibler, Nature 403, 2000) is a synthetic three-gene oscillatory circuit. Quorum sensing couples repressilators across cells — structurally identical to Kuramoto coupling with chemical diffusion as the coupling channel.

Identity Coherence

The SSGF identity model treats cognitive traits (working style, reasoning patterns, values) as oscillators whose synchronisation defines coherent identity. Chimera states (partial coherence) model cognitive dissonance. An application of the SCPN identity-coherence framework to AI self-modelling.

Musical Acoustics

Harmonic modes of musical instruments (fundamental, overtones) form coupled oscillators. Consonance = integer frequency ratios = specific phase relationships. Rhythmic groove emerges from synchronised beat subdivisions. Large & Palmer, Ecological Psychology 14(1-2), 2002.

Network Security

Normal network traffic oscillates with diurnal and weekly periods. DDoS attacks disrupt these patterns — anomalous synchronisation in packet arrivals signals coordinated attack traffic. Phase-based detection complements rate-based methods.

Robotic CPG

Central Pattern Generators produce rhythmic locomotion via coupled oscillators. Quadruped gaits (walk, trot, gallop) correspond to specific phase relationships between leg CPGs — exactly Kuramoto with discrete symmetry-breaking modes. Ijspeert, Neural Networks 21(4), 2008.

Satellite Constellation

Satellites in constellation maintain orbital slot phasing and inter-satellite link timing. Orbital mechanics produces oscillatory relative motion; communication link synchronisation requires phase coordination across the constellation.

Sleep Architecture

EEG power in delta, theta, alpha, and beta bands defines AASM sleep stages. The order parameter R computed per band tracks transitions between wake, N1, N2, N3, and REM — a natural Kuramoto hierarchy with sleep stage = regime.

Vortex Shedding

Karman vortex streets behind bluff bodies produce periodic lift and drag oscillations at the Strouhal frequency. Multiple cylinders interact via wake coupling — Stuart-Landau amplitude dynamics capture lock-in and vortex-induced vibration. Williamson & Govardhan, Annual Review of Fluid Mechanics 36, 2004.

Agent Coordination

Multiple software agents and a human operator working on a shared codebase exhibit oscillatory task patterns — heartbeat liveness checks, task flow cycles, topic focus shifts. Synchronisation = coordinated parallel work; desynchronisation = merge conflicts and wasted effort.

Phase Extraction Rationale

Domain Source Signal Extraction Phase =
EEG Voltage time series Bandpass + Hilbert Instantaneous phase
Power grid PMU phasor Direct measurement Rotor angle delta
Cardiac Intracardiac EGM Activation time mapping Activation phase
Rotating Accelerometer Order tracking + FFT Harmonic phase
Chemical T, C, P sensors Detrend + Hilbert Oscillation phase
Plasma Mirnov coils, ECE Mode fitting Mode phase
Manufacturing SPC sensor Detrend around setpoint Deviation phase
Queue Queue depth Detrend + Hilbert Demand phase
Circadian Clock gene expression Cosinor fit Acrophase
Traffic Signal state Cycle normalisation Cycle phase
Epidemic Case counts Detrend + Hilbert Wave phase
Biology Multi-modal sensors Scale-appropriate Per-scale phase
Geometry Graph node index Ring mapping theta=2pis/N Node phase
Fusion Diagnostic signals Observable mapping Equilibrium phase
Laser array Optical field Heterodyne interferometry Optical phase
PLL clock VCO output Phase detector VCO phase
Firefly Flash events Inter-flash interval Flash phase
Swarm IMU heading Compass reading Heading angle
Autonomous vehicles Headway distance Detrend + Hilbert Following phase
Brain connectome fMRI BOLD / EEG Bandpass + Hilbert Regional phase
Financial markets Price returns Hilbert transform Asset phase
Gene oscillator Fluorescence reporter Peak detection Expression phase
Identity coherence Trait activation signals Inter-event frequency Trait phase
Musical acoustics Audio waveform FFT harmonic tracking Harmonic phase
Network security Packet timestamps Inter-arrival frequency Traffic phase
Robotic CPG Joint angle encoders Direct measurement Joint phase
Satellite constellation Orbital position Kepler elements Orbital phase
Sleep architecture EEG band power Bandpass + Hilbert Band phase
Vortex shedding Pressure/force transducer Detrend + Hilbert Shedding phase
Agent coordination Heartbeat timestamps Inter-event frequency Agent liveness phase

Good/Bad Layer Partition

Domain Good (R up = healthy) Bad (R up = pathological)
EEG Alpha, gamma, network Delta (wake), beta excess
Power grid Generator sync, area freq Load demand, renewable
Cardiac SA node, atrial Ventricular desync
Rotating Shaft at nominal Blade flutter, structural
Chemical Heat transfer, feed flow Kinetics oscillation
Plasma Transport barrier, current Turbulence, sawteeth
Manufacturing Machine, line Sensor (drift = bad)
Queue Throughput (macro) Retry burst (micro)
Circadian SCN core, peripheral Behavioural desync (jet lag)
Traffic Corridor (green wave) Intersection (gridlock), demand
Epidemic Intervention coordination Infection wave, mobility
Biology Tissue, organ, systemic (none defined)
Geometry Local, global coherence (none defined)
Minimal Lower, upper (none defined)
Fusion Equilibrium, transport, boundary Events (sawtooth, ELM)
Laser array Single laser, array coupling External cavity (feedback)
PLL clock VCO lock, network PLL Stratum hierarchy (holdover)
Firefly Individual flash, swarm (none defined)
Swarm Heading alignment, flock direction Formation breakup
Autonomous vehicles Leader-follower platoon String instability
Brain connectome Visual, auditory, DMN sync Hypersync (seizure)
Financial markets Sector diversification Cross-asset herding (crash)
Gene oscillator Repressilator rhythm Quorum desync
Identity coherence Working style, values Cognitive dissonance (chimera)
Musical acoustics Harmonic consonance, groove Dissonance, tempo drift
Network security Normal traffic rhythm Attack synchronisation
Robotic CPG Gait phase coordination Leg collision, stumble
Satellite constellation Orbital slot, comms link Constellation breakup
Sleep architecture Delta (N3), alpha (wake) Beta excess (insomnia)
Vortex shedding Upstream wake coherence Lock-in (structural fatigue)
Agent coordination Task flow, topic alignment Merge conflicts, duplicated work

Boundary Sources

Domain Hard Boundaries Standard/Source
EEG Broadband sync < 0.9 Lehnertz (2009)
Power grid Freq +/-0.5 Hz, V 0.95-1.05 pu NERC BAL-003-2, ANSI C84.1
Cardiac HR 40-180 bpm, QT < 500 ms ACC/AHA guidelines, Roden (2004)
Rotating Vibration < 7.1 mm/s ISO 10816-3 zone C/D
Chemical T < 450 C, P < 15 bar Semenov limit, ASME VIII
Plasma q_min >= 1, beta_N <= 2.8 Kruskal-Shafranov, Troyon
Manufacturing Temp < 85 C, pressure > 2 OEM specs
Circadian Phase deviation < 3 h Clinical circadian disruption
Traffic Queue < 50 vehicles Intersection capacity
Epidemic Cases < 100/100k, hospital < 80% WHO threshold
Biology HR 40-180 bpm Clinical range
Fusion q_min >= 1, beta_N <= 2.8 Kruskal-Shafranov, Troyon
Laser array Phase variance < 0.3 rad, feedback < 0.5 Winful & Wang (1988)
PLL clock Phase error < 100 ns, drift < 10 ppm IEEE 1588, ITU-T G.811
Firefly Flash variance < 0.5 s Observational ecology
Swarm Formation error < 2 m, collision > 0.5 m Safety standards
Autonomous vehicles Headway > 1.5 s, speed delta < 10 km/h SAE J3016, ISO 22839
Brain connectome Global sync < 0.9 Lehnertz (2009)
Financial markets Drawdown < 5%, VIX < 30 Risk management
Gene oscillator Expression ratio 0.1-10x Elowitz & Leibler (2000)
Identity coherence R_identity > 0.3 SSGF threshold
Musical acoustics Intonation < 20 cents, tempo drift < 5% Perceptual thresholds
Network security Packet rate < 10x baseline IDS thresholds
Robotic CPG Joint angle limits, torque < max Actuator specs
Satellite constellation Slot drift < 0.1 deg, link margin > 3 dB ITU Radio Regulations
Sleep architecture Stage duration within AASM norms AASM manual v3
Vortex shedding Amplitude < fatigue limit, St = 0.2 +/- 0.05 ASME PTC 19.3
Agent coordination Heartbeat interval < 60 s, conflict rate < 0.1 Operational SLA

Actuator Mapping

Domain K (coupling) alpha (lag) zeta (drive) Psi (target)
EEG Connectivity Delta band lag Entrainment stim Target phase
Power grid Governor droop Load shed phase AGC bias Curtailment
Cardiac Drug coupling Vagal modulation Pacing rate Pacing target
Rotating Bearing stiffness Damper viscosity Speed setpoint --
Chemical Coolant flow Agitator speed Feed rate Jacket SP
Plasma Global coupling Turbulence lag Damping --
Manufacturing Global coupling Sensor lag Damping --
Queue Global coupling Micro lag Damping --
Circadian Inter-clock coupling Sleep schedule lag Light exposure Meal timing
Traffic Signal coordination Phase split Green wave offset Ramp metering
Epidemic Vaccination coordination Travel restriction Social measures Lockdown target
Biology Global coupling -- Entrainment Reference phase
Geometry Global coupling -- -- --
Minimal Global coupling -- -- --
Fusion Global coupling -- Entrainment --
Laser array Evanescent coupling Detuning offset Injection current Feedback phase
PLL clock Loop bandwidth Frequency trim Reference drive Phase target
Firefly Visual coupling -- Environmental light Flash target
Swarm Alignment coupling Obstacle avoidance Formation drive Target heading
Autonomous vehicles Platoon coupling Headway lag ACC setpoint Leader speed
Brain connectome Connectivity strength Propagation delay Stimulation Target region
Financial markets Portfolio correlation Sector rotation lag Hedging Risk target
Gene oscillator Quorum coupling Diffusion delay Inducer concentration --
Identity coherence Trait coupling Cognitive lag External feedback Value target
Musical acoustics Ensemble coupling Tempo offset Conductor beat Pitch target
Network security Traffic coupling Routing lag Rate limiting Baseline pattern
Robotic CPG Inter-leg coupling Gait phase offset Speed command Gait target
Satellite constellation Orbital coupling Propagation delay Thrust manoeuvre Slot target
Sleep architecture Inter-band coupling Band transition lag Light/sound stim Sleep stage
Vortex shedding Wake coupling Convective delay Flow speed --
Agent coordination Task coupling Communication lag Priority signal Coordination target

Coupling Topology Rationale

Domain Topology Rationale
EEG Symmetric, non-negative Cortical connectivity is undirected
Power grid Distance-decayed Admittance ~ 1/impedance ~ 1/distance
Cardiac Strong nearest-neighbour Gap junctions connect adjacent cells
Rotating Layer-block Mechanical path: shaft -> bearing -> structure
Chemical Dense intra-layer Heat-mass coupling is tight within reactions
Plasma Hierarchical decay Timescale separation between layers
Manufacturing Weak cross-layer Sensors are only indirectly coupled
Queue Distance-decayed Upstream/downstream proximity
Circadian Strong intra-layer Clock genes tightly coupled within SCN
Traffic Distance-decayed Adjacent intersections strongly coupled
Epidemic Weak cross-layer Regions coupled via mobility only
Biology Hierarchical decay Timescale separation across scales
Geometry Distance-decayed Graph adjacency determines coupling
Minimal Distance-decayed Default template
Fusion Hierarchical decay Timescale separation between layers
Laser array Distance-decayed Evanescent field exponential decay
PLL clock Hierarchical decay Stratum hierarchy (cascaded PLLs)
Firefly Distance-decayed Line-of-sight visual range
Swarm Distance-decayed Proximity-based communication range
Autonomous vehicles Distance-decayed V2V range limited by proximity
Brain connectome HCP-weighted Structural connectivity from diffusion MRI
Financial markets Correlation-based Asset return correlation matrix
Gene oscillator Dense intra-layer Same-cell gene products diffuse freely
Identity coherence Hierarchical decay Trait layers separated by abstraction level
Musical acoustics Strong intra-layer Harmonics of same instrument tightly coupled
Network security Distance-decayed Network topology determines traffic paths
Robotic CPG Strong nearest-neighbour Adjacent legs mechanically coupled
Satellite constellation Distance-decayed Inter-satellite link range
Sleep architecture Hierarchical decay Timescale separation between EEG bands
Vortex shedding Distance-decayed Wake interaction decays with cylinder spacing
Agent coordination Weak cross-layer Agents coupled only via shared repo

Imprint Semantics

Domain Physical Meaning Timescale Modulates
EEG Meditation training (plasticity) Weeks-months K, alpha
Cardiac Drug accumulation (pharmacokinetics) Hours-days K
Chemical Catalyst fouling/deactivation Months K
Manufacturing Tool wear history Weeks K
Circadian Chronic jet lag / shift work debt Days-weeks K, alpha
Biology Chronic exposure accumulation Days-months K, alpha
Fusion Plasma facing component erosion Weeks K
Laser array Mirror degradation (facet erosion) Months K
PLL clock Crystal aging (frequency drift) Years K, alpha
Firefly (none — memoryless dynamics) -- --
Swarm (none — stateless dynamics) -- --
Plasma (none — fast relative to wall conditioning) -- --
Power grid Transformer insulation aging (IEEE C57.91) Years K
Rotating Bearing wear (ISO 15243 spalling) Weeks-months K
Queue Service degradation (memory leaks, pool exhaustion) Hours-days K
Traffic Signal timing drift + road degradation Weeks-months K, alpha
Epidemic Waning immunity (Antia et al. 2018) Months K
Geometry (none) -- --
Minimal (none) -- --
Autonomous vehicles Tyre wear, brake fade Hours-days K
Brain connectome Synaptic plasticity (LTP/LTD) Days-weeks K, alpha
Financial markets Regime memory (bull/bear momentum) Weeks-months K
Gene oscillator Epigenetic modification Days-weeks K
Identity coherence Trait reinforcement / habit formation Weeks-months K, alpha
Musical acoustics Ensemble rehearsal (muscle memory) Days-weeks K
Network security Baseline drift (traffic pattern evolution) Days K
Robotic CPG Joint wear, actuator fatigue Weeks-months K
Satellite constellation Orbital decay, component aging Months-years K
Sleep architecture Chronic sleep debt Days-weeks K, alpha
Vortex shedding Structural fatigue accumulation Months K
Agent coordination (none — stateless coordination) -- --

Adding a New Domain

  1. Identify the oscillators: what physically oscillates?
  2. Map oscillators to layers by timescale hierarchy.
  3. Define omega values from domain physics (cite sources).
  4. Partition layers into good (sync = healthy) and bad (sync = pathological).
  5. Set boundaries from engineering standards or medical guidelines.
  6. Map actuators to physical control knobs.
  7. Decide if imprint applies (slow accumulation effects).
  8. Create binding_spec.yaml, policy.yaml, run.py, README.md.
  9. Validate: spo validate domainpacks/<name>/binding_spec.yaml.
  10. Run: python domainpacks/<name>/run.py.