and let us suppose that the point (xs, ys) is a steady state of this system so thatf (xs, ys) = g(xs, ys) = 0. We go forward from Eq. (2.44) by linearizing the equations around the steady state. That is, we write x(t) = xs + x(t) and that y(t) = ys + y(t) so that x(t) and y(t) measure the deviations from the steady state. Since the steady states are constant, we know that dx/dt = dx/dt and dy/dt = dy/dt. Now we will Taylor expandf (x, y) around the steady state and keep only the linear term:

0 0

Post a comment