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).