Logistic growth

Density-dependent growth slows toward a carrying capacity in the basic logistic model.

\frac{dN}{dt}=rN\left(1-\frac{N}{K}\right)

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Different ways to understand it

Exponential and logistic growth in populations | High school biology | Khan Academy
Khan Academy · English · Explanation
Connection evidence
Reviewed English material v2: card "Logistic Growth" at 6:21 — A more realistic model of population growth that produces an S-shaped (sigmoid) curve. It starts with exponential-like growth but slows as the population approaches the environment's carrying capacity, eventually leveling off.
Population Growth Models- Exponential, Logistic... Explained!
Brain Boost · English · Explanation
Connection evidence
Reviewed English material v1: card "Logistic growth model" at 1:15 — The logistic model is introduced as the bounded alternative to exponential growth. The slide names it "Aka sigmoidal" and associates it with competition for resources, a plateau, and carrying capacity K. The graph is S-shaped rather than J-shaped.
ODE | Population models
commutant · English · Explanation
Connection evidence
Reviewed English material v1: card "Exponential, logistic, and blow-up special cases" at 4:10 — Three examples are displayed as special cases of the same framework: the logistic equation corresponds to constant δ and β decreasing linearly with P, shown as dP/dt = kP(M-P).

More concepts to explore

Exponential growth
A constant per-capita growth rate yields exponential population change.
Lotka–Volterra models
Coupled equations represent predator–prey or competition interactions under simplified assumptions.
Ordinary differential equations
An ODE relates an unknown function of one variable to its derivatives.
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Evolutionary dynamics
Selection, mutation and interaction change trait or strategy frequencies.

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Knowledge connections

Exponential growth · Related · Map context
Lotka–Volterra models · Related · Map context
Ordinary differential equations · Prerequisite · Map context

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