dxt/dt=rxt{1-(xt/K)a)}/a ⇔ xt=K/{((K/x0)a-1)e-rt+1}1/a

plot

This model is the logistic-Gompertz hybrid model. Gilpin and Ayala (1973) produced this model. The population value converges to the K value.


r : Intrinsic Rate of Natural Increace

K : Carrying Capacity

a : a=0→Gompertz, a=1→Logistic

x0 : Initial Population

Simulation Time