Constrained basin stability for studying transient phenomena in dynamical systems

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

Research output: Contribution to journalArticle

5 Citations (Scopus)

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.
Original languageEnglish
Article number042205
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume93
Issue number4
Early online date9 Jan 2016
DOIs
Publication statusPublished - 13 Apr 2016

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dynamical systems
Dynamical system
complement
Complement
Return Time
Transient Dynamics
Nonlinear Phenomena
Early Warning
Lorenz System
carbon cycle
Linear Stability Analysis
Sustainability
Global Attractor
warning systems
Stability Analysis
Carbon
Bifurcation
Physics
Engineering
Perturbation

Keywords

  • nlin.CD

Cite this

Constrained basin stability for studying transient phenomena in dynamical systems. / Kan, Adrian van; Jegminat, Jannes; Donges, Jonathan; Kurths, Jürgen.

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 93, No. 4, 042205, 13.04.2016.

Research output: Contribution to journalArticle

Kan, Adrian van ; Jegminat, Jannes ; Donges, Jonathan ; Kurths, Jürgen. / Constrained basin stability for studying transient phenomena in dynamical systems. In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics. 2016 ; Vol. 93, No. 4.
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