Z 101 Simple Integration
DESIGNATION -Β Data Design with Business Relevance
System model "Simple Integration" is where systems thinking becomes tangible.
Most managers implicitly assume that things change on their own β that costs will stabilise, that demand will level off, that a problem will resolve itself. Z101 exposes the flaw in that assumption: a state only changes when something actively drives it. No rate, no change.
That single insight β deceptively simple β reshapes how you read a balance sheet, a capacity plan, or a project timeline. Every stock you manage in business has a rate behind it. Making that rate visible is the first step toward controlling it.
The four input types (Step, Pulse Train, Ramp, Sine) are not abstract mathematics. They are the four basic shapes of business pressure: a policy change that kicks in overnight, a recurring operational cycle, a cost that compounds, a demand that oscillates. Practising with each one builds the mental muscle to recognise them in the wild β before they surprise you.
What this model is good for: Working through Z101 trains you to ask the right question in any dynamic situation: what is the rate, and what is driving it? That question alone will make you a sharper reader of forecasts, a better challenger of assumptions, and a more effective participant in any scenario planning exercise.
This is the very starting point for building scenarios. Before you can stress-test assumptions or map system dependencies, you need to understand the underlying mathematics β and Z101 is where that understanding begins. One state, one rate, four input shapes. Master this, and every more complex model becomes readable.
For more information: Hartmut Bossel - System Zoo 1
Simple Integration
Hartmut Bossel Β· System Zoo
Interactive Simulator
System Equations
| Parameter | Meaning | Default |
|---|---|---|
| STEP | Step height (constant rate after tβ) | 0 [Z/day] |
| RAMP | Linear rate increase per day | 0 [Z/dayΒ²] |
| SINE | Sinusoidal amplitude | 0 [Z/day] |
| PULSE | Pulse amplitude per interval | 1 [Z/day] |
| FREQUENCY | Oscillation frequency | 0.1 [1/day] |
| INITIAL STATE | Z(0) | 0 [Z] |
A price increase takes effect on day 20. The state (cumulative cost) rises linearly from that point on.
Monthly delivery pulses. Inventory jumps periodically and holds until the next pulse arrives.
When a rate itself grows over time β rising labour costs, gradual capacity pressure β the state accumulates quadratically. Managers who track only totals routinely underestimate how fast things compound.
A teaching model for oscillating inputs β seasonal demand, energy cycles, supply rhythms. Real seasonality is lumpier, but the sine makes the integrator behaviour visible before adding empirical data.
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