To keep the Earth system in a desirable region of its state space, such as defined by the recently suggested "tolerable environment and development window", "guardrails", "planetary boundaries", or "safe (and just) operating space for humanity", one needs to understand not only the quantitative internal dynamics of the system and the available options for influencing it (management) but also the structure of the system's state space with regard to certain qualitative differences. Important questions are, which state space regions can be reached from which others with or without leaving the desirable region, which regions are in a variety of senses "safe" to stay in when management options might break away, and which qualitative decision problems may occur as a consequence of this topological structure?
In this article, we develop a mathematical theory of the qualitative topology of the state space of a dynamical system with management options and desirable states, 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. We suggest a certain terminology for the various resulting regions of the state space and perform a detailed formal classification of the possible states with respect to the possibility of avoiding or leaving the undesired region. Our results indicate that, before performing some form of quantitative optimization such as of indicators of human well-being for achieving certain sustainable development goals, a sustainable and resilient management of the Earth system may require decisions of a more discrete type that come in the form of several dilemmas, e.g. choosing between eventual safety and uninterrupted desirability, or between uninterrupted safety and larger flexibility.
We illustrate the concepts and dilemmas drawing on conceptual models from climate science, ecology, coevolutionary Earth system modelling, economics, and classical mechanics, and discuss their potential relevance for the climate and sustainability debate, in particular suggesting several levels of planetary boundaries of qualitatively increasing safety.
General news | 2018-03-19
In 2017, we surpassed one thousand published articles in peer-reviewed journals and we hosted the fourth international conference on resilience and sustainability science. Another year to be proud of, we think
Research news | 2018-03-14
Amid an increase in megacities, changes in ecosystems far away can affect local access to freshwater
Research news | 2018-03-12
Ten essentials for guiding action-oriented research on energy transformation and climate change
Research news | 2018-03-09
To celebrate International Women’s Day, we have been highlighting some of our women researchers at the centre. In our final profile this week, we showcase associate professor Beatrice Crona, whose work spans from small-scale fisheries governance to global drivers of change.
Research news | 2018-03-08
To celebrate International Women’s Day, we are highlighting some of our women researchers. We would now like to showcase Jennifer Hinton, a PhD candidate studying the social dynamics of a sustainable biophysical resource economy
Research news | 2018-03-08
New method to map livelihood benefits of ecosystem services for guiding future land use decisions in the Sahel