# Hutchinson's Equation

Hutchinson's Equation

In this delayed logistic equation, is the intrinsic growth rate, is the system carrying capacity, and is the adult population size at time . The growing species, for example, Daphnia, produces an egg clutch that requires the time 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.

r

k

x(t)

t

τ