I numerically integrated a 3-equation non-linear ODE system in the form:
$$ dx/dt = f_1(x,y,z) \\ dy/dt = f_2(x,y,z)\\ dz/dt = f_3(x, y, z)$$
whose appear to be stabilizing on a periodic orbit. How can i estimate the period of this orbit only looking at the sequence of "points" that i generated? I tried to register the position $(x_1,y_1,z_1)$ at a certain time $T_1$, then register the time $T_2$ where my integration produces a point $(x_2,y_2,z_2)$ that is in a "small" region around the first point, getting the period as $T = T_1 - T_2$. This approach generates strange behaviour sometimes, and i can't find anywhere a consistent method to get the unknown period of a periodic orbit. Can anyone help?
EDIT: got a new idea, can i watch the points in the phase space $(x, dx/dt)$ computed in discrete time to get the period?