In my master thesis I try to answer the following question: How fast is an environmental system allowed to change before it collapses? In our work we focus on population dynamical systems with time-scale separation, where one parameter of the system is changing with a certain velocity, whereas the other Parameter do not depend on the time. By increasing the velocity it is possible that the dynamics of the biological system, which are for all possible parameter settings in a stable state, are not able to track the equilibrium and the system collapses. The change of the model dynamics are caused by a so-called rate-induced bifurcation. Further we want to answer the questions:
- Is there a critical rate of change of the parameter? Under the critical rate the system remains in a stable state and above the rate the system collapses.
- Does the critical rate depend on the time-scale separation or other model parameter?
- Under which parameter settings the system is more resilient against the change of a model parameter with a certain speed?
- Populations dynamics
- Nonlinear dynamics
- Physical oceanography
- Martin Losch, Annika Fuchs, Jean-Francois Lemieux, Anna Vanselow: A parallel Jacobian-free Newton-Krylov solver for a coupled sea ice-ocean model. J. Comput. Physics257: 901-911 (2014)
- Singer, A., Schückel, U., Beck, M., Bleich, O., Brumsack, H.-J., Freund, H., Geimecke, C., Lettmann, K.A., Millat, G., Staneva, J., Vanselow, A., Westphal, H., Wolff, J.-O., Wurpts, A., Kröncke, I. (2016). Evaluating species distribution models with historical macrofauna data: a hindcast for the Jade Bay (North Sea, Germany). Marine Ecology Progress Series 551:13-30.