JOURNAL OF DIFFERENTIAL EQUATIONS | 卷:269 |
Bifurcations from anattracting heteroclinic cycle under periodic forcing | |
Article | |
Labouriau, Isabel S.1,2  Rodrigues, Alexandre A. P.1,2  | |
[1] Univ Porto, Ctr Matemat, Porto, Portugal | |
[2] Univ Porto, Fac Ciencias, Rua Campo Alegre 687, P-4169007 Porto, Portugal | |
关键词: Periodic forcing; Heteroclinic cycle; Global attractor; Bifurcations; Bistability; | |
DOI : 10.1016/j.jde.2020.03.024 | |
来源: Elsevier | |
【 摘 要 】
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. (c) 2020 Elsevier Inc. All rights reserved.
【 授权许可】
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