Defects in spatiotemporal diagrams and their relations to phase coherence and lack of observability

Spatiotemporal systems are commonly investigated in terms of spatiotemporal diagrams and, most often, the analysis is limited to the first instabilities. Due to the lack of a Takens-like theorem for spatiotemporal systems, the resulting dynamics is almost never interpreted using phase portraits reconstructed from one variable locally recorded. This work is an attempt to make an explicit link between reconstructed phase portraits and spatiotemporal diagrams. Defects distributions are interpreted in terms of a lack of phase coherence. The lack of a simple structure-as a torus characterized by a closed curve for Poincaré section when a quasiperiodic regime is identified-is tentatively interpreted in terms of observability. A first link is thus made between the defects distribution and the nature of the underlying dynamics.