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

plot

This logistic model is commonly used to the model of the population growth because this model is not so difficult but have reality than exponential growth model. In this model, density effect is integrated as the term of (1-xt/K). The population value converges to carrying capacity, K value.


r : Intrinsic Rate of Natural Increace

K : Carrying Capacity

x0 : Initial Population

Simulation Time