Signature of on-off intermittency in measured signals

On-off intermittency is a phase-space mechanism that allows dynamical systems to undergo bursting. As its name suggests, bursting is a phenomenon in which episodes of high activity are alternated with periods of inactivity. Here we attempt to see whether we can tell from the output of a signal when an observed bursting behavior is caused by the presence of on-off intermittency, using the example of a forced logistic map. The results of our study indicate that on-off intermittency can be readily distinguished from other mechanisms for bursting we know of, except for one. Many statistical properties of finite-length signals generated by on-off intermittency can in fact be mimicked by the output of a nonlinearly filtered, linear autoregressive random process.