Synchronization Analysis of Coupled Noncoherent Oscillators

We present two different approaches to detect and quantify phase synchronization in the case of coupled non-phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the Rössler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators.

[1]  G. Fischer,et al.  Plane Algebraic Curves , 1921, Nature.

[2]  Rabinder N Madan,et al.  Chua's Circuit: A Paradigm for Chaos , 1993, Chua's Circuit.

[3]  E Rosa,et al.  Experimental real-time phase synchronization of a paced chaotic plasma discharge. , 2000, Physical review letters.

[4]  S Boccaletti,et al.  Experimental characterization of the transition to phase synchronization of chaotic CO2 laser systems. , 2002, Physical review letters.

[5]  D. Ruelle,et al.  Recurrence Plots of Dynamical Systems , 1987 .

[6]  E. Ott,et al.  Detecting phase synchronization in a chaotic laser array. , 2001, Physical review letters.

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

[8]  Jürgen Kurths,et al.  Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography , 1998 .

[9]  R. Llinás,et al.  Experimentally determined chaotic phase synchronization in a neuronal system. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[10]  István Z Kiss,et al.  Collective dynamics of chaotic chemical oscillators and the law of large numbers. , 2002, Physical review letters.

[11]  J. Kurths,et al.  Heartbeat synchronized with ventilation , 1998, Nature.

[12]  K. Wong,et al.  Intermittent phase synchronization of coupled spatiotemporal chaotic systems. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  J. Kurths,et al.  Estimation of dynamical invariants without embedding by recurrence plots. , 2004, Chaos.

[14]  Jürgen Kurths,et al.  How much information is contained in a recurrence plot , 2004 .

[15]  A. Selverston,et al.  Synchronous Behavior of Two Coupled Biological Neurons , 1998, chao-dyn/9811010.

[16]  Bernd Blasius,et al.  Complex dynamics and phase synchronization in spatially extended ecological systems , 1999, Nature.

[17]  C. Sparrow.  The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors , 1982 .

[18]  Grigory V. Osipov,et al.  PHASE SYNCHRONIZATION EFFECTS IN A LATTICE OF NONIDENTICAL ROSSLER OSCILLATORS , 1997 .

[19]  J. Kurths,et al.  Phase Synchronization of Chaotic Oscillators by External Driving , 1997 .

[20]  H. Hilton.  Plane algebraic curves , 1921 .

[21]  J. Kurths,et al.  Comparing modern and Pleistocene ENSO-like influences in NW Argentina using nonlinear time series analysis methods , 2003, nlin/0303056.

[22]  J. Weiner,et al.  Fundamentals and applications , 2003 .

[23]  J Kurths,et al.  Phase synchronization in the forced Lorenz system. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  J. Kurths,et al.  Three types of transitions to phase synchronization in coupled chaotic oscillators. , 2003, Physical review letters.

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

[26]  H. Jürgensen.  Synchronization , 2021, Inf. Comput..

[27]  J. L. Hudson,et al.  Synchronization of non-phase-coherent chaotic electrochemical oscillations. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  J. L. Hudson,et al.  Phase synchronization and suppression of chaos through intermittency in forcing of an electrochemical oscillator. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Werner Lauterborn,et al.  Coherent Optics: Fundamentals and Applications , 1999 .

[30]  Jürgen Kurths,et al.  Influence of observational noise on the recurrence quantification analysis , 2002 .

[31]  Jürgen Kurths,et al.  Multivariate recurrence plots , 2004 .