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.