This is the classic textbook model of the population dynamics of two competing species.
It is based on a pair of differential equations, each having the same mathematical form:
dX1/dt = r1.X1.(1-b1.X1-c1.X2) dX2/dt = r2.X2.(1-b2.X2-c2.X1)
Lotka-Volterra model of competitionSally Otto, Zoology, UBC, Canada. Rather more mathematically-based analysis of the model.
