Periodic phenomena in stochastic systems – PERISTOCH

This project focuses on the effect of stochastic perturbations on oscillatory phenomena in dynamical
systems. Oscillations are present in a vast number of systems in physics, biology and chemistry.
Noise acting on these systems may drastically modify the oscillation patterns, or, in the case of
excitable systems, create oscillations that were absent in the unperturbed system. Systems displaying
oscillations are by essence irreversible, and therefore the mathematical theory of their stochastic
perturbations is still in its infancy. Recently a number of new mathematical techniques have emerged
that promise substantial progress in the description of non-reversible systems. The aim of this project is
to develop these methods further and to combine them in order to obtain effective tools for the study
of oscillations in stochastic systems. These tools will be applied to the description of oscillations in dusty
plasmas, and to several models originating in mathematical biology.