LogisticGrowth Block

Models population growth that is limited by a carrying capacity (resources).

Description

The Logistic Growth model describes population growth that is limited by a carrying capacity. Unlike exponential growth (which grows forever), logistic growth slows down as the population approaches the environment's resource limit.

Mathematical Model

dP/dt = r * P * (1 - P/K)

The change in population $P$ over time is governed by the logistic equation:

$$\frac{dP}{dt} = r \cdot P \cdot \left(1 - \frac{P}{K}\right)$$

Where:

• $P$: Population size
• $r$: Intrinsic growth rate (maximum per capita growth rate)
• $K$: Carrying capacity (maximum sustainable population)

At small $P$, the term $(1 - P/K)$ is close to 1, and the population grows exponentially. As $P$ approaches $K$, the term $(1 - P/K)$ approaches 0, and the growth stops.

Parameters

growthRate ($r$)

The per-capita growth rate when resources are unlimited.

• Default: 0.1

carryingCapacity ($K$)

The maximum population that can be supported by the environment.

• Default: 1000

initialPopulation

The starting population size at the beginning of the simulation.

• Default: 10

Ports

population (Output)

The current population size.

See Also

• PredatorPrey: For interaction between species beyond resource limitation.
• SIR: For population dynamics in the context of disease.
• Stock: The internal state of the population is modeled using a Stock.