Quantifying Sustainability in a System of Coupled Tipping Elements

Characterising sustainability has become a core challenge when trying to understand the interplay between global economical and ecological dynamics and both their mutual dependence as well as their competing requirements. Identifying and understanding warning signs that would indicate where when a system gets irrevocably out of control before this happens would be a critical tool in being able to attain a viable long-term strategy that takes the needs of both economy and ecology into account.We here explore a route towards such quantities. In the last years, the concept of empowerment has been investigated as a measure of control of an actor over its environment, i.e. the potential impact that an actor can have on its environment; in addition an extension had been proposed towards a concept of sustainable empowerment which, in addition, limits oneself only to control strategies which can be undone.We investigate both concepts inside a framework of systems of coupled elements endowed with a dynamics governed by cubic differential equations, which have been established as simple but powerful models to study sustainability. In this framework, we illustrate how the dynamical properties of such a system affect empowerment and sustainable empowerment. The results suggest that these quantities can provide relevant indicators for desirable strategies to guiding such systems under sustainability considerations.