Identifying the dynamics of complex spatio-temporal systems by spatial recurrence properties

Complex spatio-temporal systems may exhibit irregular behaviors when driven far from equilibrium. Reaction-diffusion systems often lead to the formation of patterns and spatio-temporal chaos. When a limited number of observations is available, the reconstruction and identification of complex dynamical regimes become challenging problems. A method based on spatial recurrence properties is proposed to deal with this problem: generalized recurrence plots and generalized recurrence quantification analysis are exploited to show that detection of structural changes in spatially distributed systems can be performed by setting up appropriate diagrams accounting for different spatial recurrences. The method has been tested on two prototypical systems forming complex patterns: the complex Ginzburg–Landau equation and the Schnakenberg system. This work allowed us to identify changes in the stability of spiral wave solutions in the former system and to analyze the Turing bifurcations in the latter.