Logistic Growth with Delay
Hutchinson equation: dx/dt = rx(1 − x(t−τ)/K)
Increasing delay drives oscillations → chaos
Parameters
Growth rate r:
0.80
Delay τ:
1.50
Carrying cap K:
1.00
x₀ (initial):
0.10
Reset
Pause
Time:
0
x(t):
—
r·τ:
—
Regime:
—
r·τ < π/2: stable equilibrium
r·τ = π/2 ≈ 1.57: Hopf bifurcation
r·τ > π/2: sustained oscillations
r·τ ≫ 1: complex / chaotic