title: Symbolic computations of nonlinear observability.
abstract: Observability is a very useful concept for determining whether the dynamics of complicated systems can be correctly reconstructed from a single (univariate or multivariate) time series. When the governing equations of dynamical systems are high-dimensional and/or rational, analytical computations of observability coefficients produce large polynomial functions with a number of terms that become exponentially large with the dimension and the nature of the system. In order to overcome this difficulty, we introduce here a symbolic observability coefficient based on a symbolic computation of the determinant of the observability matrix. The computation of such coefficients is straightforward and can be easily analytically carried out, as demonstrated in this paper for a five-dimensional rational system.
authors.affiliation: Institute for Complex Systems and Mathematical Biology, SUPA, University of Aberdeen, Old Aberdeen AB24 3UE, United Kingdom.
authors.forename: Ezequiel
authors.initials: E
authors.lastname: Bianco-Martinez
authors.affiliation: Institute for Complex Systems and Mathematical Biology, SUPA, University of Aberdeen, Old Aberdeen AB24 3UE, United Kingdom.
authors.forename: Murilo S
authors.initials: MS
authors.lastname: Baptista
authors.affiliation: CORIA-UMR 6614 Normandie Université, CNRS-Université et INSA de Rouen, Campus Universitaire du Madrillet, F-76800 Saint-Etienne du Rouvray, France.
authors.forename: Christophe
authors.initials: C
authors.lastname: Letellier