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Anti-phase synchronization and symmetry-breaking bifurcation of impulsively coupled oscillators.

Jiang, Haibo; Liu, Yang; Zhang, Liping; Yu, Jianjiang

Authors

Haibo Jiang

Yang Liu

Liping Zhang

Jianjiang Yu

Abstract

This paper studies the synchronization in two mechanical oscillators coupled by impacts which can be considered as a class of state-dependent impulsively coupled oscillators. The two identical oscillators are harmonically excited in a counter phase, and the synchronous (anti-phase synchronization) and the asynchronous motions are considered. One- and two-parameter bifurcations of the system have been studied by varying the amplitude and the frequency of external excitation. Numerical simulations show that the system could exhibit complex phenomena, including symmetry and asymmetry periodic solutions, quasi-periodic solutions and chaotic solutions. In particular, the regimes in anti-phase synchronization are identified, and it is found that the symmetry-breaking bifurcation plays an important role in the transition from synchronous to asynchronous motion.

Journal Article Type Article
Publication Date Oct 31, 2016
Journal Communications in nonlinear science and numerical simulation
Print ISSN 1007-5704
Electronic ISSN 1878-7274
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 39
Pages 199-208
Institution Citation JIANG, H., LIU, Y., ZHANG, L. and YU, J. 2016. Anti-phase synchronization and symmetry-breaking bifurcation of impulsively coupled oscillators. Communications in nonlinear science and numerical simulation [online], 39, pages 199-208. Available from: https://doi.org/10.1016/j.cnsns.2016.02.033
DOI https://doi.org/10.1016/j.cnsns.2016.02.033
Keywords Impact oscillators; State dependent impulsively coupled oscillators; Antiphase synchronization; Symmetry breaking bifurcation

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