Identification of bifurcations of distributed systems using Generalized Recurrence Quantification Analysis

In this paper the Generalized Recurrence Plot and Generalized Recurrence Quantification Analysis are exploited to investigate spatially distributed systems characterized by a Hopf bifurcation. Specifically, the Complex Ginzburg-Landau equation is chosen as a prototypical example. Steady state spatial pattern evolution is studied by computing the recurrence quantification parameters Determinism (DET) and Entropy (ENT) of the images representing the equation solutions and plotting them on the DET-ENT plane. A point in the DET-ENT plane identifies the signature of the dynamic system generating the spatial patterns. Such patterns consist of stable or unstable waves, depending on the value of certain physical parameters. According to the different values of these parameters, the images cluster in the DET-ENT diagram quite neatly. This allows one to reconstruct the bifurcation curve separating stable and unstable spirals in the DET-ENT plane.