TRANSFERENCIA DEL PLOMO ENTRE SANGRE, TEJIDO Y HUESOS

f[x_, y_, z_] = 
      49.3 + (2. /180)*y + 
        (7. /1800)*z - ((7. /200000) + (1088/87500) + (38/1800))*
          x
g[x_, y_, z_] = 
      (1088. /87500)*x - ((2. /180) + (4/700))*y
h[x_, y_, z_] = (7. /200000)*x - (7. /1800)*z

Cálculo de los puntos de equilibrio

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

Clasificación del punto de equilibrio

f1[x_, y_, z_] = D[f[x, y, z], x]
f2[x_, y_, z_] = D[f[x, y, z], y]
f3[x_, y_, z_] = D[f[x, y, z], z]

g1[x_, y_, z_] = D[g[x, y, z], x]
g2[x_, y_, z_] = D[g[x, y, z], y]
g3[x_, y_, z_] = D[g[x, y, z], z]

h1[x_, y_, z_] = D[h[x, y, z], x]
h2[x_, y_, z_] = D[h[x, y, z], y]
h3[x_, y_, z_] = D[h[x, y, z], z]

Matriz jacobiana

Jaco=(({{f1[1946, 1438.13, 17.514], f2[1946, 1438.13, 
                17.514], f3[1946, 1438.13, 17.514]}, {g1[1946, 1438.13, 17.514], g2[1946, 1438.13, 
                17.514], g3[1946, 1438.13, 17.514]}, {h1[1946, 1438.13, 17.514], h2[1946, 1438.13, 
                17.514], h3[1946, 1438.13, 17.514]}}))

Valores propios

Eigenvalues[Jaco]

Todos los autovalores son negativos y en consecuencia el punto de equilibrio será estable.