
LotkaVolterra Equations
Hi everyone,
I have 2 lotkavolterra equations
$\displaystyle x' = ax(1  x)  bxy $
$\displaystyle 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?

To find the equilibrium points solve:
$\displaystyle ax(1x)bxy=0$
$\displaystyle cy(1y)dxy=0$
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.