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.
This work was supported by the German Federal Ministry of Education and Research (BMBF) via the Young Investigators Group CoSy-CC2 (grant no. 01LN1306A). C.M. acknowledges the support of Bedartha Goswami, Jobst Heitzig and Tim Kittel.