Title: Stochastic Models for Analysing the Stability of Oscillators

Abstract: In many applications, mathematical modelling yields
time-dependent systems of ordinary differential equations (ODEs) or
differential algebraic equations (DAEs).  We focus on oscillators,
i.e., dynamical systems including periodic solutions. The stability of
the periodic limit cycles represents an important information. To
analyse the stability properties, we consider perturbations in the
initial values of the solution or in the right-hand side of the
system. Furthermore, the sensitivity of the solution with respect to
technical parameters of the dynamical system has often to be
determined.  We construct stochastic models to achieve global
information on stability and sensitivity of oscillators. Monte Carlo
methods are feasible to compute results of the models like expected
values or variances of the stochastic processes. Alternatively, we
apply the strategy of the generalised polynomial chaos to determine
according approximations.  Numerical simulations for systems of ODEs
and DAEs are presented using the stochastic models and the methods
based on polynomial chaos.