title: An integrative quantifier of multistability in complex systems based on ecological resilience.
abstract: The abundance of multistable dynamical systems calls for an appropriate quantification of the respective stability of the (stable) states of such systems. Motivated by the concept of ecological resilience, we propose a novel and pragmatic measure called 'integral stability' which integrates different aspects commonly addressed separately by existing local and global stability concepts. We demonstrate the potential of integral stability by using exemplary multistable dynamical systems such as the damped driven pendulum, a model of Amazonian rainforest as a known climate tipping element and the Daisyworld model. A crucial feature of integral stability lies in its potential of arresting a gradual loss of the stability of a system when approaching a tipping point, thus providing a potential early-warning signal sufficiently prior to a qualitative change of the system's dynamics.
authors.affiliation: Potsdam Institute for Climate Impact Research, Transdisciplinary Concepts &Methods - Research Domain 4, Potsdam, 14412, Germany.|Humboldt University of Berlin, Department of Physics, Berlin, 12489, Germany.
authors.forename: Chiranjit
authors.initials: C
authors.lastname: Mitra
authors.affiliation: Potsdam Institute for Climate Impact Research, Transdisciplinary Concepts &Methods - Research Domain 4, Potsdam, 14412, Germany.|Humboldt University of Berlin, Department of Physics, Berlin, 12489, Germany.|University of Aberdeen, Institute for Complex Systems and Mathematical Biology, Aberdeen, AB24 3UE, United Kingdom.|Nizhny Novgorod State University, Department of Control Theory, Nizhny Novgorod, 606950, Russia.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Kurths
authors.affiliation: Potsdam Institute for Climate Impact Research, Transdisciplinary Concepts &Methods - Research Domain 4, Potsdam, 14412, Germany.
authors.forename: Reik V
authors.initials: RV
authors.lastname: Donner