Experimental and numerical study on the basin stability of the coupled metronomes

The basin stability is an effective parameter to measure the stability of multistable system under perturbations. In this paper, we try to explore the effects of the coupling strength on the basin stability of the coupled metronomes. In two coupled non-identical metronomes, the coupling strength linearly decreases the basin stability of in-phase synchronization while increases that of the anti-phase synchronization. In three coupled metronomes, there are rich coexisting collectively dynamics as in-phase, anti-phase synchronization, quasi-period states and period 4 states. The coupling strength may still change the basin stability of these coexisting dynamics states. The results are observed in experimental systems and numerical models. Our findings are significant on understanding the multistable dynamics under noisy environment.

[1]  T. Kapitaniak,et al.  Why two clocks synchronize: energy balance of the synchronized clocks. , 2011, Chaos.

[2]  G. Hu,et al.  Three types of generalized synchronization , 2007 .

[3]  Steven H. Strogatz,et al.  Norbert Wiener’s Brain Waves , 1994 .

[4]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[5]  S H Strogatz,et al.  Coupled oscillators and biological synchronization. , 1993, Scientific American.

[6]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[7]  Weiqing Liu,et al.  Experimental study on synchronization of three coupled mechanical metronomes , 2013 .

[8]  Heidi M. Rockwood,et al.  Huygens's clocks , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[9]  Jinghua Xiao,et al.  Antiphase synchronization in coupled chaotic oscillators. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[11]  Ulrich Parlitz,et al.  Synchronization and chaotic dynamics of coupled mechanical metronomes. , 2009, Chaos.

[12]  H. Abarbanel,et al.  Generalized synchronization of chaos: The auxiliary system approach. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  Przemyslaw Perlikowski,et al.  Synchronization of clocks , 2012 .

[14]  Przemyslaw Perlikowski,et al.  Clustering and synchronization of n Huygens’ clocks , 2009 .

[15]  Peter J. Menck,et al.  How basin stability complements the linear-stability paradigm , 2013, Nature Physics.

[16]  Vreeswijk,et al.  Partial synchronization in populations of pulse-coupled oscillators. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  S. Boccaletti,et al.  Synchronization of chaotic systems , 2001 .

[18]  Jinghua Xiao,et al.  Synchronizing large number of nonidentical oscillators with small coupling , 2012 .

[19]  J. Buck,et al.  Biology of Synchronous Flashing of Fireflies , 1966, Nature.

[20]  Jinghua Xiao,et al.  Anti-phase synchronization of two coupled mechanical metronomes. , 2012, Chaos.

[21]  O. Hallatschek,et al.  Chimera states in mechanical oscillator networks , 2013, Proceedings of the National Academy of Sciences.

[22]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.