x? = x(0.02 ? 0.0004x ? 0.0012y) , y? = y (0.04 ? 0.0024x ? 0.0008y)

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, 50), node, asymptotically stable ,
(12.5, 12.5), saddle point, unstable