Abundance of Infinite Switching

• Tipo: Artigo em Revista Científica Internacional
• Data: 2023

Autores

Alexandre A P Rodrigues (Autor) FCUP; Castro, L (Autor) ICBAS

Revista

Título: SIAM Journal on Applied Dynamical Systems

Vol. 22

Páginas: 2570-2600

ISSN: 1536-0040

Editora: Society for Industrial and Applied Mathematics

Indexação

ISI Web of Knowledge - 0 Citações

Scopus - 0 Citações

Outras Informações

ID Authenticus: P-00Z-6EX

DOI: 10.1137/22m151371x

Abstract (EN): We describe a class of vector fields exhibiting abundant switching near a heteroclinic network: for every neighborhood of the network and every infinite admissible path, the set of initial conditions within the neighborhood that follows the path has positive Lebesgue measure. The proof relies on the existence of large strange attractors in the terminology of Broer, Simo, and Tatjer [Nonlinearity, 11 (1998), pp. 667-770] near a heteroclinic tangle unfolding an attracting network with a twodimensional heteroclinic connection. For our class of vector fields, any small nonempty open ball of initial conditions realizes infinite switching. We illustrate the theory with a specific one-parameter family of differential equations, for which we are able to characterize its global dynamics for almost all parameters.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 31