  A new measure to characterize stability of complex dynamical systems against
large perturbation is suggested, the stability threshold (ST). It quantifies
the magnitude of the weakest perturbation capable to disrupt the system and
switch it to an undesired dynamical regime. In the phase space, the stability
threshold corresponds to the "thinnest site" of the attraction basin and
therefore indicates the most "dangerous" direction of perturbations. We
introduce a computational algorithm for quantification of the stability
threshold and demonstrate that the suggested approach is effective and provides
important insights. The generality of the obtained results defines their vast
potential for application in such fields as engineering, neuroscience, power
grids, Earth science and many others where robustness of complex systems is
studied.
