Abundance of Infinite Switching

• Type: Article in International Scientific Journal
• Date: 2023

Authors

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

Journal

Title: SIAM Journal on Applied Dynamical Systems

Vol. 22

Pages: 2570-2600

ISSN: 1536-0040

Publisher: Society for Industrial and Applied Mathematics

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 31