On–off intermittency and coherent bursting in stochastically-driven coupled maps

On–off intermittency is a phase space mechanism for bursting in dynamical systems. Here we recall how the simple example of a logistic map with a time-dependent control parameter, considered as a dynamical variable of the system, gives rise to bursting or on–off behavior. We show that, for a given realization of the driver, a stochastically driven logistic map in the on–off intermittent regime always converges to the same temporal dynamics, independently of initial conditions. In that sense, the map is not chaotic. We then explore the behavior of two coupled on–off logistic maps, each driven by a separate random process, and show that, for a wide range of coupling strengths, bursting becomes at least partially coherent. The bursting coherence has a smooth dependence on the coupling parameter and no sharp transition from coherence to incoherence is detected. In the system of two coupled on–off maps studied here, coherent bursting is rooted in the behavior during off phases when the mapped coordinates take on extremely small values.