Synchronized pendula: From Huygens’ clocks to chimera states

This topical issue collects contribution exemplifying the recent scientific progress in understanding the dynamics of coupled pendula. The individual papers focus on different questions of present day interest in theory and applications of systems of coupled oscillators. Both theoretical and experimental studies are presented.

[1]  Francis C. Moon,et al.  Coexisting chaotic and periodic dynamics in clock escapements , 2006, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

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

[3]  R. Dilão.  Anti-phase synchronization and ergodicity in arrays of oscillators coupled by an elastic force , 2014 .

[4]  Przemyslaw Perlikowski,et al.  Clustering of Huygens' Clocks , 2009 .

[5]  Makoto Kumon,et al.  CONTROLLED SYNCHRONIZATION OF TWO 1-DOF COUPLED OSCILLATORS , 2002 .

[6]  Rui Dilão,et al.  Antiphase and in-phase synchronization of nonlinear oscillators: the Huygens's clocks system. , 2009, Chaos.

[7]  Paul Woafo,et al.  Effect of self-synchronization of DC motors on the amplitude of vibration of a rectangular plate , 2014 .

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

[9]  R. E. Lamper,et al.  Synchronization of Pendulum Clocks Suspended on an Elastic Beam , 2003 .

[10]  Ricardo Chacón,et al.  On the synchronization of chains of nonlinear pendula connected by linear springs , 2014 .

[12]  S. E. Khaikin,et al.  Theory of Oscillations , 2015 .

[13]  D. Goldobin.  Uncertainty principle for control of ensembles of oscillators driven by common noise , 2011, 1105.0829.

[14]  Alexander L. Fradkov,et al.  State estimation and synchronization of pendula systems over digital communication channels , 2014, The European Physical Journal Special Topics.

[15]  Vahid Vaziri,et al.  Experimental control for initiating and maintaining rotation of parametric pendulum , 2014 .

[16]  Jinghua Xiao,et al.  Experimental and numerical study on the basin stability of the coupled metronomes , 2014 .

[17]  Kurt Wiesenfeld.  Spontaneous synchronization in large pendulum arrays , 2014 .

[18]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[19]  Przemyslaw Perlikowski,et al.  Synchronization of two self-excited double pendula , 2014 .

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

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

[22]  Alexander L. Fradkov,et al.  Synchronization and phase relations in the motion of two-pendulum system , 2007 .

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

[25]  A. Prasad,et al.  The dynamics of co- and counter rotating coupled spherical pendula , 2014, 1403.1227.

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

[27]  H. Brand,et al.  The Amplitude Equation for the Rosensweig Instability in Magnetic Fluids and Gels , 2011, 1101.3742.

[30]  Przemyslaw Perlikowski,et al.  Huygens' odd Sympathy Experiment Revisited , 2011, Int. J. Bifurc. Chaos.

[31]  Ilʹi︠a︡ Izrailevich Blekhman,et al.  Synchronization in science and technology , 1988 .

[32]  M. Senator,et al.  Synchronization of two coupled escapement-driven pendulum clocks , 2006 .

[33]  J. Pantaleone,et al.  Synchronization of metronomes , 2002 .

[34]  Francis C. Moon,et al.  Chaotic Clocks: A Paradigm for the Evolution of Noise in Machines , 2005 .

[35]  H. Nijmeijer,et al.  Controlled synchronization of pendula , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[36]  Curtis S. Wilson,et al.  The Pendulum Clock or Geometrical Demonstrations Concerning the Motion of Pendula as Applied to Clocks , 1987 .

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

[38]  D. Rosas,et al.  Robust output synchronization of second-order systems , 2014 .

[39]  Anastasios Bezerianos,et al.  Chimera states in a two–population network of coupled pendulum–like elements , 2014 .