MODELO BRUSELATOR

f[x_, y_] := 0.7 + x^2*y - 2*x - x
g[x_, y_] := 2*x - x^2*y

PUNTOS DE EQUILIBRO

NSolve[{f[x, y], g[x, y]} == {0, 0}, {x, y}]

CLASIFICACIÓN PUNTOS DE EQUILIBRIO

f1[x_, y_] = D[f[x, y], x]
f2[x_, y_] = D[f[x, y], y]
g1[x_, y_] = D[g[x, y], x]
g2[x_, y_] = D[g[x, y], y]

Jaco1=(({{f1[0.7, 2/0.7], f2[0.7, 2/0.7]}, {g1[0.7, 2/0.7], g2[0.7, 2/0.7]}}))

Eigenvalues[Jaco1]

El punto de equilibrio P1=(0.7,2/0.7) es inestable