title: Discovering independent parameters in complex dynamical systems.
abstract: The transformation of a nonlinear dynamical system into a standard form by using one of its variables and its successive derivatives can be used to identify the relationships that may exist between the parameters of the original system such as the subset of the parameter space over which the dynamics is left invariant. We show how the size of the attractor or the time scale (the pseudo-period) can be varied without affecting the underlying dynamics. This is demonstrated for the Rössler and the Lorenz systems. We also consider the case when two Rössler systems are unidirectionally coupled and when a Lorenz system is driven by a Rössler system. In both cases, the dynamics of the coupled system is affected.
authors.affiliation: The Salk Institute for Biological Studies; 10010 North Torrey Pines Road; La Jolla, CA 92037; USA ; Institute for Neural Computation; University of California at San Diego, La Jolla, CA 92093; USA.
authors.forename: Claudia
authors.initials: C
authors.lastname: Lainscsek
authors.affiliation: The Salk Institute for Biological Studies; 10010 North Torrey Pines Road; La Jolla, CA 92037; USA ; Indiana University School of Medicine, Indianapolis, IN 46204; USA.
authors.forename: Jonathan
authors.initials: J
authors.lastname: Weyhenmeyer
authors.affiliation: The Salk Institute for Biological Studies; 10010 North Torrey Pines Road; La Jolla, CA 92037; USA ; Institute for Neural Computation; University of California at San Diego, La Jolla, CA 92093; USA.
authors.forename: Terrence J
authors.initials: TJ
authors.lastname: Sejnowski
authors.affiliation: CORIA UMR 6614 - Normandie University, CRNS-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