CIFASIS   20631
CENTRO INTERNACIONAL FRANCO ARGENTINO DE CIENCIAS DE LA INFORMACION Y DE SISTEMAS
Unidad Ejecutora - UE
artículos
Título:
Optimal reconstruction of dynamical systems: A noise amplification approach
Autor/es:
UZAL, LUCAS C.; GRINBLAT, GUILLERMO L.; VERDES PABLO F.
Revista:
PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS
Editorial:
AMER PHYSICAL SOC
Referencias:
Año: 2011 vol. 84 p. 1622301 - 1622317
ISSN:
1063-651X
Resumen:
In this work we propose an objective function to guide the search for a state space reconstruction of a dynamical system from a time series of measurements. These statistics can be evaluated on any reconstructed attractor, thereby allowing a direct comparison among different approaches: (uniform or nonuniform) delay vectors, PCA, Legendre coordinates, etc. It can also be used to select the most appropriate parameters of a reconstruction strategy. In the case of delay coordinates this translates into finding the optimal delay time and embedding dimension from the absolute minimum of the advocated cost function. Its definition is based on theoretical arguments on noise amplification, the complexity of the reconstructed attractor, and a direct measure of local stretch which constitutes an irrelevance measure. The proposed method is demonstrated on synthetic and experimental time series.