ON-OFF INTERMITTENCY - POWER SPECTRUM AND FRACTAL PROPERTIES OF TIME-SERIES

Some dynamical systems possess invariant submanifolds such that the dy namics restricted to the invariant submanifold is chaotic. This situat ion arises in systems with a spatial symmetry or in the synchronizatio n of chaotic oscillators. The invariant submanifold could become unsta ble to perturbations in the transverse directions when a parameter of the system is changed through a critical blow-our value. This could re sult 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 m odel both with and without additive noise and we derive scaling result s for the power spectral density of the on-off intermittent process an d for the box counting dimension for the set of time intervals when th e process takes on values above a given threshold. We then present num erical simulations realizing these results.