Constrained basin stability for studying transient phenomena in dynamical systems.

  title={Constrained basin stability for studying transient phenomena in dynamical systems.},
  author={Adrian van Kan and Jannes Jegminat and Jonathan F. Donges and J{\"u}rgen Kurths},
  journal={Physical review. E},
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… 

Figures from this paper

How to find simple nonlocal stability and resilience measures

Stability of dynamical systems is a central topic with applications in widespread areas such as economy, biology, physics and mechanical engineering. The dynamics of nonlinear systems may completely

Estimating nonlinear stability from time series data

Basin stability (BS) is a measure of nonlinear stability in multistable dynamical systems. BS has previously been estimated using Monte-Carlo simulations, which requires the explicit knowledge of a

Global Geometric Structure of the Transient Stability Regions of Power Systems

In this paper, a novel qualitative method is proposed to analyze the transient stability of power systems. Unlike the traditional methods, this method can illustrate the structural characteristics of

Basin stability and limit cycles in a conceptual model for climate tipping cascades

Tipping elements in the climate system are large-scale subregions of the Earth that might possess threshold behavior under global warming with large potential impacts on human societies. Here, we

Multistability and variations in basin of attraction in power-grid systems

It is shown that the observed nonmonotonic behavior is a consequence of transitions in multistability, which are related to changes in stability of the \emph{unsynchronized} states, and suggest that a comprehensive understanding of changes inMultistability are necessary to prevent the unexpected catastrophic instability in the building blocks of power grids.

Topology of sustainable management of dynamical systems with desirable states : from defining planetary boundaries to safe operating spaces in the Earth system

A mathematical theory of the qualitative topology of the state space of a dynamical system with management options and desirable states is developed, as a complement to the existing literature on optimal control which is more focussed on quantitative optimization and is much applied in both the engineering and the integrated assessment literature.

Sample-Based Methods of Analysis for Multistable Dynamical Systems

This paper describes how sample based algorithms can be utilized to obtain better understanding of complex dynamical phenomena, especially in multistable dynamical systems that are difficult for analytical investigations.

Entire stability region estimation using the invariant manifolds and singularities at infinity

This study provides a new perspective to study the formation and wholeness of the stability region of power systems. The main idea of the approach proposed in this study is to project the system into



Earth system analysis : integrating science for sustainability : complemented results of a symposium organized by the Potsdam Institute (PIK)

Eart System Analysis Natural Dimensions Ecology and the Earth System Climate Change and Land Use: Global and Regional Analyses Sustainable Development in Agricultural Landscapes. Human Dimensions


It is shown that the full set of hydromagnetic equations admit five more integrals, besides the energy integral, if dissipative processes are absent, which made it possible to formulate a variational principle for the force-free magnetic fields.

Advanced Methods for Decision Making and Risk Management in Sustainability Science

Preface Climate Protection Strategies under Ambiguity about Catastrophic Consequences An Introduction to Viability Theory and Management of Renewable Resources Qualitative Modelling Techniques to

Annual Review of Ecology and Systematics

This book contains proceedings of the Annual Review of Ecology and Systematics. Topics covered include: global change, world environment, ecology, ecosystems, interactions, pollutants and climatic

Annual review of ecology, evolution, and systematics

Twenty-four articles by biologists, ecologists, and other scientists represent a year's progress in the field of paleobiogeography, genetics and geographic structure, and time as an ecological resource are addressed.

Proceedings of the National Academy of Sciences, USA

Nature in London

The article tells about the diversity of green spaces in London, the citizens’ attitude toward these spaces, and what Russian cities can learn from this experience.

IL-13受体α2降低血吸虫病肉芽肿的炎症反应并延长宿主存活时间[英]/Mentink-Kane MM,Cheever AW,Thompson RW,et al//Proc Natl Acad Sci U S A


Environ. Res. Lett

  • Environ. Res. Lett
  • 2013

J. Atmos. Sci

  • J. Atmos. Sci
  • 1963