Phase Synchronization in Regular and Chaotic Systems: a Tutorial

In this contribution we present a brief introduction to the theory of synchronization of self-sustained oscillators. Classical results for synchronization of periodic motions and eeects of noise on this process are reviewed and compared with recently found phase synchronization phenomena in chaotic oscillators. The basic notions of phase and frequency locking are reconsidered within a common framework. Application of phase synchronization to data analysis is discussed.

[1]  W. Gerstner,et al.  Time structure of the activity in neural network models. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  Jürgen Kurths,et al.  On phase Synchronization by periodic Force in Chaotic oscillators with saddle Equilibria , 2000, Int. J. Bifurc. Chaos.

[3]  Jürgen Kurths,et al.  Analysing Synchronization Phenomena from Bivariate Data by Means of the Hilbert Transform , 1998 .

[4]  M. L. Cartwright,et al.  Forced oscillations in nearly sinusoidal systems , 1948 .

[5]  Tong Kun Lim,et al.  PHASE JUMPS NEAR A PHASE SYNCHRONIZATION TRANSITION IN SYSTEMS OF TWO COUPLED CHAOTIC OSCILLATORS , 1998 .

[6]  Balth. van der Pol,et al.  VII. Forced oscillations in a circuit with non-linear resistance. (Reception with reactive triode) , 1927 .

[7]  Anishchenko,et al.  Mean Switching Frequency Locking in Stochastic Bistable Systems Driven by a Periodic Force. , 1995, Physical review letters.

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

[9]  Jürgen Kurths,et al.  Alternating Locking Ratios in Imperfect Phase Synchronization , 1999 .

[10]  L Schimansky-Geier,et al.  Synchronization of noisy systems by stochastic signals. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  David A. Rand,et al.  Bifurcations of the forced van der Pol oscillator , 1978 .

[12]  Giuseppe Rega,et al.  An exploration of chaos , 1996 .

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

[14]  Mark Hess,et al.  TRANSITION TO PHASE SYNCHRONIZATION OF CHAOS , 1998 .

[15]  N. Longridge,et al.  Computerised dynamic posturography: its place in the evaluation of patients with dizziness and imbalance. , 1994, The Journal of otolaryngology.

[16]  R. G. Medhurst,et al.  Topics in the Theory of Random Noise , 1969 .

[17]  T. Geisel,et al.  Delay-induced multistable synchronization of biological oscillators , 1998 .

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

[19]  S. Strogatz,et al.  Synchronization of pulse-coupled biological oscillators , 1990 .

[20]  E. M. Hickin.  Modulation, Noise and Spectral Analysis , 1966 .

[21]  H H Abel,et al.  Synchronization in the human cardiorespiratory system. , 1998, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[22]  Michael Rosenblum,et al.  Human Postural Control: Force Plate Experiments and Modelling , 1998 .

[23]  A. Andronow,et al.  Zur Theorie des Mitnehmens von van der Pol , 1930 .

[24]  J Cernácek.  Stabilography in neurology. , 1980, Agressologie: revue internationale de physio-biologie et de pharmacologie appliquees aux effets de l'agression.

[25]  P. Grassberger,et al.  Symmetry breaking bifurcation for coupled chaotic attractors , 1991 .

[26]  Mw Hirsch,et al.  Chaos In Dynamical Systems , 2016 .

[27]  R. L. Stratonovich.  OSCILLATOR SYNCHRONIZATION IN THE PRESENCE OF NOISE , 1965 .

[28]  P. Landa.  Nonlinear Oscillations and Waves in Dynamical Systems , 1996 .

[29]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[30]  Dmitry E. Postnov,et al.  INTERACTING COHERENCE RESONANCE OSCILLATORS , 1999 .

[31]  E. Mosekilde,et al.  TRANSVERSE INSTABILITY AND RIDDLED BASINS IN A SYSTEM OF TWO COUPLED LOGISTIC MAPS , 1998 .

[32]  Arkady Pikovsky,et al.  Forcing oscillatory media: phase kinks vs. synchronization , 1999 .

[33]  Raymond Kapral,et al.  Synchronization Defects and Broken Symmetry in Spiral Waves , 1997, chao-dyn/9712003.

[34]  C. Hayashi,et al.  Nonlinear oscillations in physical systems , 1987 .

[35]  J. Kurths,et al.  Attractor-Repeller Collision and Eyelet Intermittency at the Transition to Phase Synchronization , 1997 .

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