Identifying homoclinic orbits in the dynamics of intermittent signals through recurrence quantification

Abstract

In this paper, we show how the phenomenon of intermittency observed in systems with turbulent flow-sound interaction is related to the formation of homoclinic orbits in the phase space. Such orbits that emerge via the intersection of the stable and unstable manifold of an equilibrium configuration result from interactions that happen at multiple spatial/temporal scales associated with turbulent convection and wave propagation. Through a quantification of the time spent by the dynamics in the aperiodic states using recurrence plots, we show how the presence of homoclinic orbits in the dynamics may be convincingly demonstrated, which is often not possible through a visual inspection of the phase space of the attractor.