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

Abstract

PublishedThis 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.This work is partially supported by the National Natural Science Foundation of China (Grant nos. 11402224, 11202180, 61273106 and 11171290), the Natural Science Foundation of Jiangsu Province of China (Grant no. BK20151295), the Qin Lan Project of the Jiangsu Higher Education Institutions of China, and the Jiangsu Overseas Research and Training Program for University Prominent Young and Middle-aged Teachers and Presidents. We also thank Mr. Marcin Kapitaniak for helpful discussion