Periodic Forcing of a Heteroclinic Network

• Type: Article in International Scientific Journal
• Date: 2021

Authors

Isabel S Labouriau (Author) FCUP; Alexandre A P Rodrigues (Author) FCUP

Journal

Title: Journal of Dynamics and Differential Equations

Vol. 35

Pages: 2951-2969

ISSN: 1040-7294

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: P-00V-7V5

DOI: 10.1007/s10884-021-10054-w

Abstract (EN): We present a comprehensive mechanism for the emergence of rotational horseshoes and strange attractors in a class of two-parameter families of periodically-perturbed differential equations defining a flow on a three-dimensional manifold. When both parameters are zero, its flow exhibits an attracting heteroclinic network associated to two periodic solutions. After slightly increasing both parameters, while keeping a two-dimensional connection unaltered, we focus our attention in the case where the two-dimensional invariant manifolds of the periodic solutions do not intersect. We prove a wide range of dynamical behaviour, ranging from an attracting quasi-periodic torus to rotational horseshoes and Henon-like strange attractors. We illustrate our results with an explicit example.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 19