| Code | System | Business Examples | |
|---|---|---|---|
| Z101 | β« | Single integration |
π ProcurementCumulative spend accumulates as purchase orders are placed over time.
π ProductionFinished goods inventory builds up as units roll off the production line.
π» SaaSTotal MRR accumulates as new subscriptions are activated each month.
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| Z102 | βοΈ | System state and state change |
π ProcurementSupplier contract status shifts between active, under review, and expired.
π ProductionWork-in-progress moves between production stages as throughput changes.
π» SaaSARR changes as upgrades, downgrades, and churns alter subscription value.
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| Z103 | π | Exponential growth and decay |
π ProcurementSupplier base shrinks exponentially as a preferred-vendor consolidation programme cuts the tail.
π ProductionMachine degradation accelerates exponentially as deferred maintenance compounds.
π» SaaSUser base grows exponentially during viral product-led growth (PLG) phases.
|
| Z104 | β³ | Exponential delay |
π ProcurementNew vendors only reach full capacity output after a smoothed supplier onboarding ramp-up.
π ProductionA quality-improvement initiative lowers defect rate gradually, not instantly.
π» SaaSFeature adoption by existing users lags its release date by a smoothed diffusion delay.
|
| Z105 | π | Time-dependent growth |
π ProcurementAnnual purchase volume ramps seasonally as Q4 budget spend accelerates toward year-end.
π ProductionCapacity ramps over a fixed investment horizon as new lines come online in stages.
π» SaaSTrial-to-paid conversions follow a time-bounded free-trial window with a deadline forcing function.
|
| Z106 | πΎ | Simple population dynamics |
π ProcurementActive supplier count grows (new approvals) and shrinks (de-listings) as a simple stock.
π ProductionWorkforce headcount driven by hiring rate minus attrition rate.
π» SaaSActive user base governed by new sign-ups minus account cancellations.
|
| Z107 | π¦ | Infection dynamics |
π ProcurementMaverick spending spreads virally as non-compliant purchasing behaviour is copied across teams.
π ProductionA production defect propagates through batches before quality control catches it.
π» SaaSViral product adoption: each active user recruits new users via referral or word of mouth.
|
| Z108 | πͺ£ | Overloading a buffer β |
π ProcurementPurchase order backlog overflows when approval throughput is slower than submission rate.
π ProductionIn-process queue at a bottleneck machine overflows when arrival rate exceeds cycle time.
π» SaaSSupport ticket queue floods when inbound tickets exceed agent resolution capacity.
|
| Z109 | πΎ | Logistic growth with constant harvest |
π ProcurementApproved supplier pool grows logistically but is continuously pruned by a fixed annual vendor review.
π ProductionSkilled workforce grows logistically while a constant number retire or resign each year.
π» SaaSSubscriber base expands within a market ceiling while a fixed number of contracts expire monthly.
|
| Z110 | π | Logistic growth with stock-dependent harvest |
π ProcurementSupplier relationships grow but churn rate rises proportionally as the portfolio becomes harder to manage.
π ProductionProduct line grows logistically; complexity-driven scrap rate scales with portfolio size.
π» SaaSUser base grows but churn rate increases with size as the customer success team is stretched thin.
|
| Z111 | π¬ | Density-dependent growth (Michaelis-Menten) |
π ProcurementSavings realisation rate saturates as easy-win categories are optimised and diminishing returns set in.
π ProductionThroughput gain from adding workers saturates due to fixed equipment constraints (bottleneck saturation).
π» SaaSNew feature adoption saturates as the addressable user segment willing to adopt it is exhausted.
|
| Z112 | π | Double integration and exponential delay |
π ProcurementDemand signal takes two lagged steps (forecast β order β delivery) before reaching supplier production.
π ProductionCapacity investment decisions lag demand signals, causing double-delay in capacity matching.
π» SaaSRevenue lags pipeline build which itself lags marketing spend β a two-stage delay to bookings.
|
| Z113 | π | Transition from one state to another |
π ProcurementSupplier qualification: vendors transition from "prospective" to "approved" over a vetting process.
π ProductionProducts move from raw material β WIP β finished goods as production stages complete.
π» SaaSLeads transition through funnel stages: visitor β trial β paid β expanded account.
|
| Z114 | γ°οΈ | Linear oscillator of second order |
π ProcurementInventory bullwhip: order quantities oscillate as buyers over-correct in response to perceived shortages.
π ProductionProduction scheduling oscillates between over- and under-capacity as planners react to backlog signals.
π» SaaSHeadcount planning oscillates as hiring surges are followed by freeze periods in response to growth signals.
|
| Z115 | πΊοΈ | State space diagram |
π ProcurementMapping supplier risk score vs. spend concentration to visualise portfolio exposure regions.
π ProductionOEE vs. WIP level phase plot to identify operating regimes (stable, congested, starved).
π» SaaSChurn rate vs. NPS phase plane to diagnose product-market fit trajectories.
|
| Z116 | π | Triple integration and exponential delay |
π ProcurementThree-tier supply chain delay: demand β tier-1 order β tier-2 production β raw material procurement.
π ProductionCapital project pipeline: investment approval β engineering β construction β capacity goes live.
π» SaaSThree-stage revenue lag: content marketing β lead β opportunity β closed-won revenue.
|
| Z117 | π΅ | Linear oscillator of third order |
π ProcurementMulti-echelon bullwhip: oscillations amplify across a three-tier supply chain due to triple integration delays.
π ProductionHireβtrainβproduce cycle creates third-order oscillations in output as workforce adjustments ripple through.
π» SaaSSpend β pipeline β revenue β reinvestment cycle oscillates when feedback gains are mistuned.
|
| Code | System | Business Examples | |
|---|---|---|---|
| Z201 | π‘ | Rotating pendulum |
π ProcurementSpot vs. contract sourcing pendulum swings between extremes as commodity prices cycle.
π ProductionMake vs. buy decisions rotate through insource/outsource cycles driven by cost and capacity dynamics.
π» SaaSBuild vs. buy technology strategy oscillates as in-house capability and vendor market mature.
|
| Z202 | π | Oscillator with limit cycle (van der Pol) |
π ProcurementSupplier negotiation cycles stabilise into a recurring self-sustaining pattern of price reviews and re-bids.
π ProductionShift scheduling settles into a self-sustaining overtimeβrecovery pattern when buffers are small.
π» SaaSSprint velocity stabilises into a limit cycle of crunch and cool-down periods each quarter.
|
| Z203 | βοΈ | Brusselator |
π ProcurementSourcing strategy oscillates between centralise and decentralise driven by autocatalytic internal politics.
π ProductionQuality initiatives and defect rates interact in self-reinforcing oscillation when inspection resources are limited.
π» SaaSTechnical debt and feature velocity interact autocatalytically: more debt slows delivery, reducing revenue, cutting investment in debt repayment.
|
| Z204 | π± | Bistable oscillator |
π ProcurementDual-source vs. single-source strategy flips between two stable modes depending on risk threshold.
π ProductionFacility operates in either "normal run" or "expedite mode" β two stable states with hysteresis between.
π» SaaSProduct strategy locks into either "growth mode" or "efficiency mode" with a tipping-point transition.
|
| Z205 | πͺοΈ | Chaotic bistable oscillator (Duffing) |
π ProcurementCommodity price under periodic supply shocks exhibits chaotic switching between high and low price regimes.
π ProductionDemand-driven scheduling under seasonal forcing creates chaotic fluctuation between over- and under-capacity.
π» SaaSChurn and expansion revenue driven by periodic campaigns show chaotic sensitivity to campaign timing.
|
| Z206 | π¦οΈ | Heat, weather, and chaos (Lorenz) |
π ProcurementGlobal commodity markets exhibit Lorenz-like sensitivity: small geopolitical events cause unpredictable price spirals.
π ProductionInterplay of demand, capacity, and inventory in a multi-echelon network produces chaotic, weather-like fluctuations.
π» SaaSThree coupled metrics (acquisition, activation, retention) exhibit sensitive dependence β small onboarding changes cascade chaotically into LTV.
|
| Z207 | π¦ | Chaotic attractor (RΓΆssler) |
π ProcurementSupplier pricing, lead time, and quality oscillate around a strange attractor under periodic contract renegotiations.
π ProductionWIP, throughput, and cycle time spiral around a chaotic attractor when production control is loosely tuned.
π» SaaSSales velocity, pipeline coverage, and quota attainment evolve chaotically when incentive structures create non-linear feedback.
|
| Z208 | β‘ | Coupled dynamos and chaos |
π ProcurementTwo interdependent procurement hubs (Europe and Asia) mutually amplify ordering chaos through shared suppliers.
π ProductionTwo coupled production lines sharing a common buffer can generate chaotic throughput swings.
π» SaaSTwo competing SaaS products sharing a developer ecosystem drive each other into chaotic release cadences.
|
| Z209 | π€Έ | Balancing an inverted pendulum |
π ProcurementJust-in-time procurement is inherently unstable: without continuous rebalancing, stockouts or excess build up rapidly.
π ProductionLean zero-buffer production requires continuous active scheduling to remain on target β it cannot run on autopilot.
π» SaaSMaintaining CAC:LTV balance in a high-growth phase requires constant active adjustment of spend and pricing.
|
| Z210 | πͺ | Optimizing glider flight: search for thermals |
π ProcurementCategory managers search for cost-saving opportunities (thermals) while managing baseline spend (glide path).
π ProductionLean improvement teams seek efficiency pockets while sustaining baseline OEE during exploration.
π» SaaSGrowth teams alternate between exploiting high-converting channels (thermals) and exploring new acquisition vectors.
|
| Z211 | βοΈ | Flight dynamics |
π ProcurementStrategic sourcing has pitch (cost focus), roll (risk balance), and yaw (supplier diversity) axes of control.
π ProductionPlant operations steered across three axes: throughput rate, quality level, and schedule adherence.
π» SaaSCompany trajectory governed by three coupled controls: revenue growth, burn rate, and NPS β analogous to lift, drag, and thrust.
|
| Z212 | π | House heating dynamics |
π ProcurementSupplier pipeline is "heated" by sourcing activity and cools through attrition β thermostat logic controls intake rate.
π ProductionProduction rate is throttled like a thermostat to maintain target inventory level against variable demand (heat loss).
π» SaaSOnboarding pipeline is kept "warm" by marketing; churn acts as heat loss; the CS team acts as the thermostat.
|
| Z213 | π₯ | Integral relations and heat conduction |
π ProcurementCost pressure propagates through supply chain tiers like heat conduction β slowly diffusing from buyer to sub-tier suppliers.
π ProductionProcess improvement diffuses spatially across a factory floor as knowledge spreads between work centres.
π» SaaSChurn risk conducts from power users to casual users as product value erodes β visible in cohort heat maps.
|
| Z214 | π¨ | Boundary layer flow |
π ProcurementPolicy compliance drops near the "edges" of the organisation (remote teams, small spend categories) like a boundary layer.
π ProductionQuality consistency degrades near shift boundaries and handover points β analogous to boundary layer turbulence.
π» SaaSUser engagement thins near the edges of product usage (low-frequency users, edge features) mirroring laminar-to-turbulent boundary flow.
|