x? = x(0.04 ? 0.0008x ? 0.004y) , y? = y (0.1? 0.005x ? 0.002y)

Question

Let x and y represent the populations (in thousands) of two species that share a
habitat. For each system of equations, find and assess the stability of the
equilibrium points. Remember that, for real populations, both x0 and y0 must be
nonnegative for ( x0, y0) to be an equilibrium point.

Answer 1

(0, 0), node, unstable ;
(50, 0), node, asymptotically stable ;
(0, 500), node, asymptotically stable