Influence of the singular manifold of non observable states in reconstructing chaotic attractors

Madalin Frunzete 1 Jean-Pierre Barbot 2, 3 Christophe Letellier 4
1 ECS-lab EA 3649
ECS-Lab - Électronique et Commande des Systèmes Laboratoire
3 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : It is known that the reconstructed phase portrait of a given system strongly depends on the choice of the observable. In particular, the ability to obtain a global model from a time series strongly depends on the observability provided by the measured variable. Such a dependency results from i) the existence of a singular observability manifold for which the coordinate transformation ii) how often the trajectory visits the neighborhood of the observability singularity manifold (OSM). In order to clarify how these aspects contribute to the observability coefficients, we introduce the probability of visits of OSM and the relative time spent in OSM to construct a new coefficient. Combined with the symbolic observability coefficients previously introduced by one of the authors.
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Madalin Frunzete, Jean-Pierre Barbot, Christophe Letellier. Influence of the singular manifold of non observable states in reconstructing chaotic attractors. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2012, 86 (2). ⟨hal-00750595⟩

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