Characterization of a periodically driven chaotic dynamical system

We discuss how to characterize the behaviour of a chaotic dynamical system depending on a parameter that varies periodically in time, such that the time scale of the periodic variation of the parameter is much larger than the `internal' time scale. In particular, we study the predictability time, the correlations and the mean responses, by defining a local-in-time version of these quantities. We find that the local quantities strongly depend on the phase of the cycle. In this case, the standard global quantities can give misleading information.