Exploring instability in complex systems - simulations in no-man's land

The prediction and analysis of sudden changes in complex systems and models (called tipping) are a current topic in science and an urgent problem for society. A few hotly debated examples are the possible collapse of the Gulf Stream, the sudden loss of vegetation in nutrient-polluted lakes, or the change between the vegetated and desert state in dry regions. While these cases of tipping are well understood in idealised mathematical models, their analysis is restricted in field observations, laboratory experiments and complex model simulations by the impossibility to systematically explore dynamically unstable phenomena. For many complex systems the notion of equilibrium is only defined in a statistical mechanics sense as an emerging phenomenon, which, by its definition, must be stable.

The proposed research will develop general mathematical methods that will remove these restrictions: they will enable experimenters and modellers to discover and track unstable phenomena in laboratory experiments and complex model simulations, or, more generally, in any situation where one can provide input into the system depending on its output in real time. Two features distinguish the systems under study from the idealised models.

* (Limited input only) One has input into the system but may not be able to set the entire internal state at will.
* (Variability) The experiment or model run is repeatable, but the system has internal variability such that outputs are affected by randomness or disturbances.

Several areas will serve as testbeds and springboards to the wider scientific community: individual-based models in ecology, epidemiology and social science, vibration tests in engineering, models of climate subsystems, and abstract spatially extended systems (such as used for neuron population models).

The research will have immediate impact on several other scientific disciplines such as ecology, epidemiology, neuroscience and climate modelling. Engineering research on new experimental techniques and model validation will also benefit directly from achievement of the objectives. The methods developed during the project will enable modellers and experimenters in both areas to discover new evidence for or against hypothesised underlying nonlinear mechanisms (such as tipping) and make new predictions, for example, about transition probabilities between different states. Dissemination of the results will be through publications in journals and presentations at conferences in the respective application areas.

Impact on society and economy will come mainly through uptake of the research in the above-mentioned disciplines. The new mathematical and experimental tools for gathering evidence and validating models will be used in science and engineering to inform policy-making and industrial testing.
To broaden the potential impact of the proposed research the PI will initiate collaboration with two groups that have a proven track record of research with high impact beyond academia: the Aquatic Ecology group at TU Wageningen and the Mechanical Engineering group of JJ Thomsen and I Santos at DTU Lyngby. The TUW group's research on tipping (to which the proposed research is directly relevant) spans modelling, controlled laboratory and large-scale experiments, field work and policy advice. The DTU group has already invested in prototype experiments to which the newly developed methods can be directly applied. Their development of hardware for non-contact real-time feedback control and software for continuation of unstable vibrations in experiments is directly guided by industry needs. The PI has secured support from external collaborators with experimental know-how and industry contacts (David Barton and Jens Starke, see letters of support), which supports knowledge transfer between the DTU group and the PI's project.

The knowledge transfer between DTU and TUW and the PI's research group will flow both ways since the PI will also dedicate time to spend on problems and models specific to the collaborators' research.

To ensure that the outcomes of the research are accessible to end users in science and engineering (within and outside of academia) all general-purpose software elements will be made publicly available on open-source software repositories (such as Sourceforge, where the PI currently maintains DDE-Biftool).

Several application areas of the proposed research (climate, ecology, epidemiology) and the underlying mathematical themes (tipping, instability) lend themselves naturally to popularisation and public presentation. The PI will visit local schools and contribute to science popularisation initiatives such as Pint of Science.