1:1 Mode locking and generalized synchronization in mechanical oscillators

We describe the relation between the complete, phase and generalized synchronization of the mechanical oscillators (response system) driven by the chaotic signal generated by the driven system. We identified the close dependence between the changes in the spectrum of Lyapunov exponents and a transition to different types of synchronization. The strict connection between the complete synchronization (imperfect complete synchronization) of response oscillators and their phase or generalized synchronization with the driving system (the (1:1) mode locking) is shown. We argue that the observed phenomena are generic in the parameter space and preserved in the presence of a small parameter mismatch.

[1]  Parlitz,et al.  Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. , 1996, Physical review letters.

[2]  J. Kurths,et al.  From Phase to Lag Synchronization in Coupled Chaotic Oscillators , 1997 .

[3]  Carroll,et al.  Driving systems with chaotic signals. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[4]  T. Kapitaniak,et al.  Synchronization of chaos using continuous control. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Kestutis Pyragas.  Predictable chaos in slightly perturbed unpredictable chaotic systems , 1993 .

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

[7]  T. Carroll,et al.  MASTER STABILITY FUNCTIONS FOR SYNCHRONIZED COUPLED SYSTEMS , 1999 .

[8]  Michael Rosenblum,et al.  Synchronization and chaotization in interacting dynamical systems , 1995 .

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

[10]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  Przemyslaw Perlikowski,et al.  Ragged synchronizability of coupled oscillators. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[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]  Mauricio Barahona,et al.  Synchronization in small-world systems. , 2002, Physical review letters.

[14]  Przemyslaw Perlikowski,et al.  Synchronization of coupled mechanical oscillators , 2006 .

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

[16]  Alexander B. Neiman,et al.  Nonlinear Dynamics of Chaotic and Stochastic Systems: Tutorial and Modern Developments , 2003 .

[17]  Carson C. Chow,et al.  Small Worlds , 2000 .

[18]  Gesine Reinert,et al.  Small worlds , 2001, Random Struct. Algorithms.

[19]  Tomasz Kapitaniak,et al.  Synchronization of mechanical systems driven by chaotic or random excitation , 2003 .

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