C. Letellier, J. Maquet, H. Labro, L. Le Sceller, G. Gouesbet, F. Argoul & A. Arneodo
Analyzing chaotic behaviour in a Belousov-Zhabotinskii reaction by using a global vector field reconstruction,
Journal of Physical Chemistry A, 102, 10265-10273, 1998.
C. Letellier, L. Le Sceller & G. Gouesbet
Nonlinear dynamics : what for ?
Journal of High Temperature Material Processes, 2, 83-101, 1998.
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.
Abstract. In practical problems of phase-space reconstruction, it is usually the case that the reconstruction is much easier using a particular recorded scalar variable. This seems to contradict the general belief that all variables of a dynamical system are equivalent in phase-space reconstruction problems. This paper will argue that, in many cases, the choice of a particular scalar time series from which to reconstruct the original dynamics could be critical. It is argued that different dynamical variables do not provide the same level of information (observability) of the underlying dynamics and, as a consequence, the quality of a global reconstruction critically depends on the recorded variable. Examples in which the choice of observables is critical are discussed and the level of information contained in a given variable is quantified in the case where the original system is known. A clear example of such a situation arises in the Rössler system for which the performance of a global vector field reconstruction technique is investigated using time series of variables x, y or z, taken one at a time.
P. Reiterer, C. Lainscsek, F. Schürrer, C. Letellier & J. Maquet
A Nine-Dimensional Lorenz System to study high-dimensional chaos,
Journal of Physics A, 31, 7121-7139, 1998.