  Transient dynamics are of large interest in many areas of science. Here, a
generalization of basin stability (BS) is presented: constrained basin
stability (CBS) that is sensitive to various different types of transients
arising from finite size perturbations. CBS is applied to the paradigmatic
Lorenz system for uncovering nonlinear precursory phenomena of a boundary
crisis bifurcation. Further, CBS is used in a model of the Earth's carbon cycle
as a return time-dependent stability measure of the system's global attractor.
Both case studies illustrate how CBS's sensitivity to transients complements BS
in its function as an early warning signal and as a stability measure. CBS is
broadly applicable in systems where transients matter, from physics and
engineering to sustainability science. Thus, CBS complements stability analysis
with BS as well as classical linear stability analysis and will be a useful
tool for many applications.
