Critical bursting

Abstract

We present a deterministic mechanism to generate random bursts. It is illustrated using a low-dimensional dynamical system, derived for the problem of zero-Prandtl-number thermal convection, that shows a direct bifurcation from the motionless state to a time-dependent regime. The flow kinetic energy involves random peaks with power law histogram and frequency spectrum. We show that this results from the existence of exact exponentially growing solutions and propose this as an elementary deterministic mechanism to generate random bursts. Contrary to SOC models, we consider a low-dimensional continuous dynamical system without any prescribed threshold dynamics.