262. Stocks Flows

The foundation of system dynamics modeling. Two element types:

Stocks change only through flows. Flows change instantaneously based on system state.

262.1. Mathematical foundation

For a stock with inflow rate and outflow rate :

In integral form:

Each stock obeys this conservation law: change in stock = net flow.

262.2. Units

Dimensional consistency is mandatory:

A model with mismatched units is wrong; checking units catches half of all SD modeling errors.

262.3. Three classes of stock-flow systems

First-order linear:

Equivalently: stock decays toward with time constant . Examples: exponential decay (radioactive substance), goal-seeking (workforce hiring toward target).

Second-order linear: two stocks, coupled

Eigenvalues determine behavior: stable / unstable spirals, exponential growth/decay, oscillation. Predator-prey, mass-spring, etc.

Nonlinear: with nonlinear — limit cycles, chaos, bifurcations. Most real-world systems.

262.4. Bathtub metaphor

A common teaching tool: a bathtub with a tap (inflow) and drain (outflow). Water level = stock. Tap and drain rates = flows.

Even simple bathtubs are non-intuitive: most people overestimate how fast filling a bathtub increases water level, because they fail to integrate the flow over time.

262.5. Stocks have memory; flows don’t

If you turn off the tap (set inflow to zero), the bathtub doesn’t suddenly empty — water remains. Same with inventory after halting production, or accumulated CO2 after stopping emissions. Stocks persist.

Conversely, a flow can change instantaneously: stop the inflow → inflow rate is zero immediately.

This distinction is fundamental: policy interventions on flows have delayed effects on stocks.

262.6. Connection to differential equations

Stocks and flows = the language of ordinary differential equations (ODEs). SD diagrams are just an alternative notation for systems of ODEs. The visual language helps:

262.7. See also