System-Dynamics
Example: Cooling a hot cup of coffee. Stock: Coffee temperature $T$. Flow: Heat loss to the environment $kT$. Behavior: Temperature decreases towards room temperature $T_{\rm room}$. Equation: $$\tag{SD3} \frac{dT}{dt} = -k(T - T_{\rm room}), $$ where $k$ is the cooling rate. Diagram: graph LR; Coffee -->|Loses Heat| Environment Environment -->|Gains Heat| CoffeeExample: Population growth with feedback. Stock: Population $P$ Flow: Birth rate proportional to population, where $r$ is the growth rate, then more people lead to more births, reinforcing growth. Behavior: Exponential growth. Equation: $$\tag{SD2} \frac{dP}{dt} = rP. $$ Diagram: graph LR; Population -->|Influences| BirthRate BirthRate -->|Increases| PopulationExample: Population growth without feedback. Stock: Population $P$ Flow: Birth rate $b$ (constant). Behavior: Population increases at a steady rate. Equation: $$\tag{SD1} \frac{dP}{dt} = b. $$ Diagram: graph TD; Population -->|+ Constant Birth Rate| Population