Hastings-Powell Food Chain Chaos
Three-trophic-level ecological chaos: prey, predator, top-predator
Parameters
a₁ (prey→pred):
5.00
a₂ (pred→top):
0.10
b₁ (half-sat prey):
3.00
b₂ (half-sat pred):
2.00
d₁ (pred death):
0.40
d₂ (top death):
0.01
Reset
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.