{ diff(x1, t) = (1*k13*k1*x1*(1 - (x1 + x2)/k2) + (-1)*k13*k3*x1*x3/(x1 + x2 + k4) + (-1)*k13*k5*x1*x4/(k6 + x4))/k13,
  diff(x2, t) = (1*k13*k3*x1*x3/(x1 + x2 + k4) + (-1)*k13*k8*x2*x4/(k6 + x4) + (-1)*k13*k7*x2)/k13,
  diff(x3, t) = ((-1)*k13*k3*x1*x3/(x1 + x2 + k4) + 1*k13*k9*k7*x2 + (-1)*k13*k10*x3)/k13,
  diff(x4, t) = (1*k13*k11 + (-1)*k13*k12*x4)/k13 }