Lotka-Volterra Equations

An ecological model which assumes that a population $x$ increases at a rate $dx = Ax\,dt$, but is destroyed at a rate $dx=-Bxy\,dt$. Population $y$ decreases at a rate $dy=-Cy\,dt$, but increases at $dy=Dxy\,dt$, giving the coupled differential equations

$${dx\over dt}=Ax-Bxy$$

$${dy\over dt}=-Cy+Dxy.$$

Critical points occur when $dx/dt=dy/dt=0$, so

$$A-By=0$$

$$-C+Dx=0.$$

The sole Stationary Point is therefore located at $(x,y)=(C/D,A/B)$.