Bifurcations from anattracting heteroclinic cycle under periodic forcing

• Type: Article in International Scientific Journal
• Date: 2020

Authors

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

Journal

Title: Journal of Differential Equations

Vol. 269

Pages: 4137-4174

ISSN: 0022-0396

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 6 Citations

Scopus - 6 Citations

Other information

Authenticus ID: P-00R-ZGD

DOI: 10.1016/j.jde.2020.03.024

Abstract (EN): There are few examples of non-autonomous vector fields exhibiting complex dynamics that may be proven analytically. We analyse a family of periodic perturbations of a weakly attracting robust heteroclinic network defined on the two-sphere. We derive the first return map near the heteroclinic cycle for small amplitude of the perturbing term, and we reduce the analysis of the non-autonomous system to that of a two-dimensional map on a cylinder. Interesting dynamical features arise from a discrete-time Bogdanov-Takens bifurcation. When the perturbation strength is small the first return map has an attracting invariant closed curve that is not contractible on the cylinder. Near the centre of frequency locking there are parameter values with bistability: the invariant curve coexists with an attracting fixed point. Increasing the perturbation strength there are periodic solutions that bifurcate into a closed contractible invariant curve and into a region where the dynamics is conjugate to a full shift on two symbols.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 38