On-off intermittency: Power spectrum and fractal properties of time series

Some dynamical systems possess invariant submanifolds such that the dynamics restricted to the invariant submanifold is chaotic. This situation arises in systems with a spatial symmetry or in the synchronization of chaotic oscillators. The invariant submanifold could become unstable to perturbations in the transverse directions when a parameter of the system is changed through a critical blow-out value. This could result in an extreme form of temporally intermittent bursting called on-off intermittency. We propose a model that incorporates the universal features of systems that display on-off intermittency. We study this model both with and without additive noise and we derive scaling results for the power spectral density of the on-off intermittent process and for the box counting dimension for the set of time intervals when the process takes on values above a given threshold. We then present numerical simulations realizing these results.