/* Linear 2D example with a nonlinear perturbation in the 1st equation */
f: a*x+b*y;
g: c*x+d*y;

J: jacobian([f,g],[x,y]);
J0:J,y=0;

determinant(J0-matrix([L,0],[0,L]));

expand(%);

coeff(%,L);

%o6, L=0;

/* Next, add a nonlinear term that preserves (0,0) as an equilibrium point. */
f2: a*x+b*y+c*y^3;

J2: jacobian([f2,g],[x,y]);

J2, x=0, y=0; /* evaluate at (0,0) */;

/* same jacobian, same eigenvalues, so see above! */