  Stochastic differential equations describe well many physical, biological and
sociological systems, despite the simplification often made in their
derivation. Here the usage of simple stochastic differential equations to
characterize and classify complex dynamical systems is proposed within a
Bayesian framework. To this end, we develop a dynamic system classifier (DSC).
The DSC first abstracts training data of a system in terms of time dependent
coefficients of the descriptive stochastic differential equation. Thereby the
DSC identifies unique correlation structures within the training data. For
definiteness we restrict the presentation of DSC to oscillation processes with
a time dependent frequency {\omega}(t) and damping factor {\gamma}(t). Although
real systems might be more complex, this simple oscillator captures many
characteristic features. The {\omega} and {\gamma} timelines represent the
abstract system characterization and permit the construction of efficient
signal classifiers. Numerical experiments show that such classifiers perform
well even in the low signal-to-noise regime.
