This project focuses on questions of stability and metastability for stochastic dynamical networks. On the one hand, in view of the high complexity of large networks as they occur in many applications, we will extend the approach of isospectral transformations for deterministic dynamical networks to a variety of stochastic networks. The goal is to simplify a given network systematically in such a way that its stability or metastability can be studied for the simpler network. On the other hand, we will address the effect of noise on the dynamical properties of certain classes of networks such as feed-forward networks and coupled Hamiltonian systems.
Simon Holbach PDF
Positive Harris recurrence for degenerate diffusions with internal variables and randomly perturbed time-periodic input