Constrained basin stability for studying transient phenomena in dynamical systems

Adrian van Kan, Jannes Jegminat, Jonathan Donges, Jürgen Kurths

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


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.
Original languageEnglish
Article number042205
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number4
Early online date9 Jan 2016
Publication statusPublished - 13 Apr 2016

Bibliographical note

8 pages, 5 figures

Aknowledgements: The research reported in this article was developed
within the working group “Complex systems perspectives on anthropogenic climate change” at the Naturand Ingenieurwissenschaftliches Kolleg sponsored by the German National Academic Foundation (Studienstiftung des deutschen Volkes) and in the scope of the COPAN project on coevolutionary pathways at the Potsdam Institute for Climate Impact Research. JFD thanks the Stordalen Foundation (via the Planetary Boundary Research Network and the Earth League’s EarthDoc program for financial support. We thank two anonymous
referees for their useful comments which helped to improve the readability of this paper and we are grateful for insightful discussions with Jobst Heitzig and Boyan Beronov.


  • nlin.CD


Dive into the research topics of 'Constrained basin stability for studying transient phenomena in dynamical systems'. Together they form a unique fingerprint.

Cite this