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Hi everyone,
I have 2 lotka-volterra equations
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:
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.