Lotka-Volterra two-species competition model

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)

where:
X₁,X₂ are the populations sizes of the two species;
r₁,r₂ are the intrinsic rate sof increase of the two species;
b₁,b₂ are the self-inhibition coefficients for the two species;
c₁,c₂ are the competitor’s inhibition coefficient for each species.