  Diverse complex dynamical systems are known to exhibit abrupt regime shifts
at bifurcation points of the saddle-node type. The dynamics of most of these
systems, however, have a stochastic component resulting in noise driven regime
shifts even if the system is away from the bifurcation points. In this paper,
we propose a new quantitative measure, namely, the propensity transition point
as an indicator of stochastic regime shifts. The concepts and the methodology
are illustrated for the one-variable May model, a well-known model in ecology
and the genetic toggle, a two-variable model of a simple genetic circuit. The
general applicability and usefulness of the method for the analysis of regime
shifts is further demonstrated in the case of the mycobacterial switch to
persistence for which experimental data are available.
