Complex network analysis of forced synchronization in a hydrodynamically self-excited jet

Previous experiments by Li and Juniper (2013) have shown that a hydrodynamically self-excited jet can synchronize with external acoustic forcing via one of two possible routes: a saddle-node (SN) bifurcation or a torus-death (TD) bifurcation. In this study, we use complex networks to analyze and forecast these two routes to synchronization in a prototypical self-excited flow – an axisymmetric low-density jet at an operating condition close to its first Hopf point. We build the complex networks using two different methods: the visibility algorithm and the recurrence condition. We find that the networks built with the visibility algorithm are high-clustering, hierarchical, and assortative in the degree of their vertices, although only the TD networks are scale free. Nevertheless, we find that the assortativity coefficient is a sufficiently sensitive indicator by which to distinguish between the SN and TD routes to synchronization and to forecast the onset of synchronization. As for the networks built with the recurrence condition, we find that their topological features differ between the two routes to synchronization, but vary predictably along either route. We quantify these variations using statistical measures such as the mean degree, spectral radius, and transitivity dimension. This study shows that complex networks can be a useful tool for distinguishing between the SN and TD routes to synchronization, and for forecasting the proximity of a system to its synchronization boundaries. These findings could open up new opportunities for complex networks to be used in the development of open-loop control strategies for hydrodynamically self-excited flows.