ODE (deterministic):
Ẋ = αX − βXY
Ẏ = δXY − γY
Stochastic (Gillespie):
Rates: birth(X)=α·X
death(X)=β·X·Y
birth(Y)=δ·X·Y
death(Y)=γ·Y
Fixed pt: X*=γ/δ, Y*=α/β
Noise ~ 1/√N → extinction risk
Ẋ = αX − βXY
Ẏ = δXY − γY
Stochastic (Gillespie):
Rates: birth(X)=α·X
death(X)=β·X·Y
birth(Y)=δ·X·Y
death(Y)=γ·Y
Fixed pt: X*=γ/δ, Y*=α/β
Noise ~ 1/√N → extinction risk
0.60
0.08
0.06
0.50
15
X: 0 | Y: 0