Hutchinson's Equation

growth rate

r

0.16

carrying capacity

k

1.1

time

τ

10

In this delayed logistic equation,

r

is the intrinsic growth rate,

k

is the system carrying capacity, and

x(t)

is the adult population size at time

t

. The growing species, for example, Daphnia, produces an egg clutch that requires the time

τ

to become adults. Depending on the values of the parameters, the system displays equilibrium, growing oscillation, steady oscillation, or decaying oscillation. Each of these behaviors can be correlated with the formation of attractors as seen in the phase diagram.