Convergence criteria of oscillating curve

Hi all,
i've done a series of simulations; given the high number of simulations, i would like to automate the process of the solution analysis.

The output of each simulation is an oscillating curve.
i would like to find an algorithm to determine if the oscillations are stable, unstable,...
the curve is stable if the amplitude of the oscillation is not diverging.
I would also like to know if some of the curves are similar to a beat (beat phenomenon in vibration theory).

is there any matlab builtin function that could help me? Otherwise, do you know some mathematic criteria that i could implement?

Thank you in advanced! =)