Equilibrium Point #4:

> RANGE4 := x=3.31..3.35, y=6.6..6.75;

> DEplot( MODEL, VARS, DOMAIN, RANGE4, arrows=MEDIUM, title=`Direction Field Near (10/3,20/3)` );

>

The matrix for the linearized system at this equilibrium point is:

> A := subs( x=10/3, y=20/3, evalm(J) );

>

The eigenvalues of this matrix are:

> eigenvals( A );

> evalf(%);

Since there is one positive and one negative eigenvalue, the origin is an unstable saddle for the linearized and (10/3,20/3) is a saddle for the nonlinear system. This is consistent with the direction field that focuses on the portion of the phase portrait close to this equilibrium solution. (Can you see the two straight line solutions?)

>