title: Constrained basin stability for studying transient phenomena in dynamical systems.
abstract: 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.
authors.affiliation: Department of Physics and Astronomy, University of Heidelberg, Im Neuenheimer Feld 226, D-69120 Heidelberg, Germany.|Department of Physics, Imperial College London, Prince Consort Rd, London SW7 2BB, United Kingdom.
authors.forename: Adrian
authors.initials: A
authors.lastname: van Kan
authors.affiliation: Department of Physics and Astronomy, University of Heidelberg, Im Neuenheimer Feld 226, D-69120 Heidelberg, Germany.
authors.forename: Jannes
authors.initials: J
authors.lastname: Jegminat
authors.affiliation: Potsdam Institute for Climate Impact Research, P.O. Box 601203, D-14412 Potsdam, Germany.|Stockholm Resilience Centre, Stockholm University, Kräftriket 2B, 114 19 Stockholm, Sweden.
authors.forename: Jonathan F
authors.initials: JF
authors.lastname: Donges
authors.affiliation: Potsdam Institute for Climate Impact Research, P.O. Box 601203, D-14412 Potsdam, Germany.|Department of Physics, Humboldt University Berlin, Newtonstr. 15, D-12489 Berlin, Germany.|Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3FX, United Kingdom.|Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 606950 Nizhny Novgorod, Russia.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Kurths