Logistic Population Growth — Continuous & Discrete
⛶
Mode
Continuous time — dN/dt = rN(1−(N/K)^θ)
Discrete time — Nₜ₊₁ = Nₜ + rNₜ(1−(Nₜ/K)^θ)
Bifurcation diagram (vary r)
Effect of population density
Initial population N₀
10
Growth rate r
0.6
Discrete model gets cycles/chaos as r rises above ~2.
Carrying capacity K
100
Shape θ
1
Number of steps
40
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Logistic growth over time
Cursor: X =
–
, Y =
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