Hastings-Powell Food Chain Chaos

Three-trophic-level ecological chaos: prey, predator, top-predator

Parameters

t: 0
x (prey):
y (pred):
z (top):
Hastings-Powell (1991):
ẋ = x(1−x) − a₁xy/(b₁+x)
ẏ = a₁xy/(b₁+x) − a₂yz/(b₂+y) − d₁y
ż = a₂yz/(b₂+y) − d₂z

First demonstration of chaos in a food chain. The strange attractor lives in (x,y,z)∈[0,1]³. Chaos requires at least 3 trophic levels.