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Attractor information for discrete dynamical systems by means of optimal discrete Galerkin bases |
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| Authors: | Francisco J Solis Rosa I Sánchez |
| Institution: | 1. L2S, CNRS, Supelec, Univ Paris-Sud, 3 rue Joliot-Curie, 91192 Gif-sur-Yvette, France;2. Institut Universitaire de France, 103 bld Saint-Michel, 75005 Paris, France;1. Direction Générale de l''Armement, Techniques Navales Brest, BCRM de Brest, 29240 Brest Cedex 9, France;2. ENSTA Bretagne, Lab-STICC, 2 rue François Verny, 29806 Brest, France;1. Autonomous Systems Research Theme, The University of Manchester, M13-9PL, Manchester, United Kingdom;2. Laboratoire Angevin de Recherche en Ingénierie des Systèmes, The University of Angers, 40 Rue de Rennes, 49035 Angers, France |
| Abstract: | We introduce local adaptive discrete Galerkin bases as a basis set in order to obtain geometrical and topological information about attractors of discrete dynamical systems. The asymptotic behavior of these systems is described by the reconstruction of their attractors in a finite dimensional Euclidean space and by the attractor topological characteristics including the minimal embedding dimension and its local dimension. We evaluate numerically the applicability of our geometrical and topological results by examining two examples: a dissipative discrete system and a nonlinear discrete predator–prey model that includes several types of self-limitation on the prey. |
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