Lotka-Volterra Predator-Prey
Lotka 1925, Volterra 1926 — Oscillating populations in phase space
Parameters
α (prey growth):
0.80
β (predation rate):
0.20
δ (pred efficiency):
0.10
γ (pred death):
0.40
Initial prey x₀:
10
Initial pred y₀:
5
Noise σ:
0.0
Logistic prey (K):
off
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dx/dt = αx − βxy (prey)
dy/dt = δxy − γy (predator)
Equilibrium: x*=γ/δ, y*=α/β
Phase portrait
: closed orbits.
Noise breaks orbits — real stochasticity.