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

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

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.

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

• Journal Article Type: Article
• Acceptance Date: Feb 28, 2016
• Online Publication Date: Mar 5, 2016
• Publication Date: Oct 31, 2016
• Deposit Date: May 25, 2016
• Publicly Available Date: Mar 6, 2017
• 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
• DOI: https://doi.org/10.1016/j.cnsns.2016.02.033
• Keywords: Impact oscillators; State dependent impulsively coupled oscillators; Antiphase synchronization; Symmetry breaking bifurcation
• Public URL: http://hdl.handle.net/10059/1485