Synchronization of self-sustained oscillators inertially coupled through common damped system

Abstract We study the dynamics of two self-oscillating systems inertially coupled to a linear oscillator. This interaction mechanism results in various types of synchronous motions such as in-phase, anti-phase and phase synchronization. We demonstrate the existence of mono-stable regimes and multi-stable behavior with two or more coexisting attractors. We present the bifurcational analysis revealing transition mechanisms between these regimes. In the multi-stable case, we examine the role of coupling parameter and shape of oscillations (the parameter indicating nonlinearity and strength of the damping) in various structure formations of attraction basins.

[1]  J. Carlson,et al.  The Pendulum Clock. , 1991 .

[2]  J. Kurths,et al.  Automatic control of phase synchronization in coupled complex oscillators , 2005, Proceedings. 2005 International Conference Physics and Control, 2005..

[3]  A. B. Cawthorne,et al.  STIMULATED EMISSION AND AMPLIFICATION IN JOSEPHSON JUNCTION ARRAYS , 1999 .

[4]  Theodore Sizer,et al.  Neodymium lasers as a source of synchronized high-power optical pulses , 1988 .

[5]  Howard C. Howland,et al.  Dynamics of two van der Pol oscillators coupled via a bath , 2004 .

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

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

[8]  K. Wiesenfeld,et al.  Synchronization law for a van der Pol array. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Alexander L. Fradkov,et al.  Control of the coupled double pendulums system , 2005 .

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

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

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

[13]  Knut Graichen,et al.  Swing-up of the double pendulum on a cart by feedforward and feedback control with experimental validation , 2007, Autom..

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

[15]  Giovanni Filatrella,et al.  The mechanism of synchronization of Josephson arrays coupled to a cavity , 2002 .

[16]  Matthäus Staniek,et al.  Measuring Synchronization in the Epileptic Brain: a Comparison of Different Approaches , 2007, Int. J. Bifurc. Chaos.

[17]  J. Kurths,et al.  Synchronization in Oscillatory Networks , 2007 .

[18]  Belykh,et al.  Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  V. N. Belykh,et al.  Chaotic dynamics of two Van der Pol-Duffing oscillators with Huygens coupling , 2009 .