Model reduction for slow-fast stochastic systems with bistability by Maria Bruna, Oxford
Huxley 140, 16:00-17:00
The quasi-steady-state approximation (or stochastic averaging principle) is a useful tool in the study of multiscale stochastic systems, giving a practical method by which to reduce the number of degrees of freedom in a model. We extend this method to slow–fast systems in which the fast variables exhibit metastable behaviour. The key parameter that determines the form of the reduced model is the ratio of the timescale for the switching of the fast variables between metastable states to the timescale for the evolution of the slow variables. Our approach uses a perturbation analysis at the level of the Fokker–Planck equation for the joint probability density. The method is illustrated using two simple examples (a chemical switch and a prey-predator system), and tested with several numerical simulations.
Mathematical Models of Crowded Ion Transport by Martin Burger, University of Münster
Huxley 140, 17:00-18:00
The understanding and control of transport through ion channels is a highly relevant problem in physiology, to which mathematical modeling and simulation can essentially contribute. In this talk we discuss models based on modifications of the Poisson-Nernst-Planck equations to include crowding effects. Besides issues in the basic model derivation, we discuss the analysis, numerical simulation, and finally some relevant inverse problem.