# Math Help - Lotka-Volterra Equations

1. ## Lotka-Volterra Equations

Hi everyone,
I have 2 lotka-volterra equations

$x' = ax(1 - x) - bxy$
$y' = cy(1 - y) - dxy$

where x and y is the population of the species normalised by the carrying capacity of the ecosystem. a,b,c,d are positive constants.

How do I determine the equilibrium points of the system, and whether or not these points are stable?

2. To find the equilibrium points solve:

$ax(1-x)-bxy=0$
$cy(1-y)-dxy=0$

simultaneously. Next need to linearize them and then solve for the eigenvalues of the resulting matrix. The form of the eigenvalues determines the type of equilibrium point. May I suggest "Differential Equations" by Blanchard, Devaney, and Hall". I think it does a nice job of explaining these in great detail at a confortable level. I'll try and work on it today and see what I get.