A great number of techniques developed for studying nonlinear dynamical systems start with the embedding of a scalar time series, lying on an m-dimensional
object, in an embedding space of dimension d. In a number of practical situations, the choice of the observable does matters for our ability to extract dynamical information from the embedded attractor.
To quantify the observability, we estimate observability indices which have direct bearing on standard problems in nonlinear dynamics such as model building, control techniques and synchronization.
Luis Aguirre directs the MACSIN group which is one of the research groups at Universidade Federal de Minas Gerais (Belo Horizonte, Brazil). The MACSIN group is concerned with various aspects of modeling, analysis and control of systems which display nonlinear dynamics and chaos, control of systems.
Our collaboration is supported by CNRS and CNPq since 1999. It is now supported by PICS 4923 entitled From nonlinear dynamics to biomedicine : techniques for investigating the cardio-respiratory system.
C. Letellier, J. Maquet, L. Le Sceller, G. Gouesbet & L. A. Aguirre, On the non-equivalence of observables in phase space reconstructions from recorded time series, Journal of Physics A, 31, 7913-7927, 1998.
C. Letellier & L. Aguirre, Investigating nonlinear dynamics from time series : the influence of symmetries and the choice of observables, Chaos, 12, 549-558, 2002.
C. Letellier, L. A. Aguirre, J. Maquet & Aziz-Alaoui, Should all the species of a food chain be counted to investigate the global dynamics ?, Chaos, Solitons & Fractals, 13, 1099-1113, 2002.
J. Maquet, C. Letellier & L. A. Aguirre, Scalar modeling and analysis of a 3D biochemical reaction model, Journal of Theoretical Biology, 228 (3), 421-430, 2004.
C. Letellier, L. A. Aguirre & J. Maquet, Relation between observability and differential embeddings for nonlinear dynamics, Physical Review E, 71, 066213, 2005.
L. A. Aguire & C. Letellier, Observability of multivariate differential embeddings, Journal of Physics A, 38 (28), 6311-6326, 2005.