predator-prey system with harvesting
x(t) = predator
y(t) = prey
Consider two scenarios for h, firstly when h is proportional to y, say ey and secondly, when h=N, where N is a constant.
1)For the case when h is proportional to the densitly of the prey, how does the solution differ from that when h =0?
2)For the case when the harvesting rate is constant, h =N, find the equilibrium points, how many if these are in the phase plane? examine the stability of the paths close to the equilibrium points in the phase plane.
i have found equilibrium points, community martix, eigenvalues and stability for when h=0 and when h=ey of 1) but am not sure how to find the eigen vectors.
in part 2 i have found the equilibrium points but can't manage the rest>
any help would be much appretiated thanks.