Phase coherence in an ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses.

An ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses shows a range of nontrivial behavior, from synchronization, desynchronization, to clustering. The group behavior that arises in the ensemble can be predicted from the phase response of a single oscillator to a given impulsive perturbation. We present a theory based on phase reduction of a jump stochastic process describing a Poisson-driven limit-cycle oscillator, and verify the results through numerical simulations and electric circuit experiments. We also give a geometrical interpretation of the synchronizing mechanism, a perturbative expansion to the stationary phase distribution, and the diffusion limit of our jump stochastic model.

[1]  勇一 作村,et al.  Biophysics of Computation , 2001 .

[2]  Yasuhiro Tsubo,et al.  Synchrony of neural oscillators induced by random telegraphic currents. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Roy,et al.  Experimental synchronization of chaotic lasers. , 1994, Physical review letters.

[4]  Arkady Pikovsky,et al.  Synchronization of self-sustained oscillators by common white noise , 2005 .

[5]  Keijin Sato,et al.  Noise-induced synchronization of uncoupled nonlinear systems , 2006 .

[6]  Hiroya Nakao,et al.  Reproducibility of a Noisy Limit-Cycle Oscillator Induced by a Fluctuating Input (Oscillation, Chaos and Network Dynamics in Nonlinear Science--Proceeding of the International Symposium on Nonlinear Oscillations) , 2006 .

[7]  Thomas M. Antonsen,et al.  On-off intermittency: power spectrum and fractal properties of time series , 1996 .

[8]  H. Risken.  The Fokker-Planck equation : methods of solution and applications , 1985 .

[9]  Jürgen Kurths,et al.  Noise-induced phase synchronization and synchronization transitions in chaotic oscillators. , 2002, Physical review letters.

[10]  S. Sharma,et al.  The Fokker-Planck Equation , 2010 .

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

[12]  Arkady Pikovsky,et al.  Statistics of trajectory separation in noisy dynamical systems , 1992 .

[13]  Donald L. Snyder,et al.  Random point processes , 1975 .

[14]  S. Swain.  Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences , 1984 .

[15]  Christof Koch,et al.  Biophysics of Computation: Information Processing in Single Neurons (Computational Neuroscience Series) , 1998 .

[16]  K. N. Dollman,et al.  - 1 , 1743 .

[17]  Floyd B. Hanson,et al.  Applied stochastic processes and control for jump-diffusions - modeling, analysis, and computation , 2007, Advances in design and control.

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

[19]  R K Powers,et al.  Relationship between simulated common synaptic input and discharge synchrony in cat spinal motoneurons. , 2001, Journal of neurophysiology.

[20]  Tetsuya J. Kobayashi,et al.  Melanopsin-dependent photo-perturbation reveals desynchronization underlying the singularity of mammalian circadian clocks , 2007, Nature Cell Biology.

[21]  Jun-nosuke Teramae,et al.  Noise Induced Phase Synchronization of a General Class of Limit Cycle Oscillators(Oscillation, Chaos and Network Dynamics in Nonlinear Science) , 2006 .

[22]  L. Goddard.  Information Theory , 1962, Nature.

[23]  Atsushi Uchida,et al.  Consistency of nonlinear system response to complex drive signals. , 2004 .

[24]  Arkady Pikovsky,et al.  Antireliability of noise-driven neurons. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  C. W. Gardiner,et al.  Handbook of stochastic methods - for physics, chemistry and the natural sciences, Second Edition , 1986, Springer series in synergetics.

[26]  Khashayar Pakdaman,et al.  The Reliability of the Stochastic Active Rotator , 2002, Neural Computation.

[27]  Arkady Pikovsky,et al.  Synchronization and desynchronization of self-sustained oscillators by common noise. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Hirokazu Fujisaka,et al.  A New Intermittency in Coupled Dynamical Systems , 1985 .

[29]  E. Wong,et al.  ON THE RELATION BETWEEN ORDINARY AND STOCHASTIC DIFFERENTIAL EQUATIONS , 1965 .

[30]  Ralf Stannarius,et al.  On-off Intermittency in Stochastically Driven Electrohydrodynamic Convection in Nematics , 1999, patt-sol/9902004.

[31]  H. Fujisaka,et al.  Stability Theory of Synchronized Motion in Coupled-Oscillator Systems , 1983 .

[32]  Claudio R. Mirasso,et al.  Analytical and numerical studies of noise-induced synchronization of chaotic systems. , 2001, Chaos.

[33]  D. Williams.  STOCHASTIC DIFFERENTIAL EQUATIONS: THEORY AND APPLICATIONS , 1976 .

[34]  Arthur T. Winfree,et al.  Unclocklike behaviour of biological clocks , 1975, Nature.

[35]  H. Risken.  Fokker-Planck Equation , 1996 .

[36]  G Bard Ermentrout,et al.  Efficient estimation of phase-resetting curves in real neurons and its significance for neural-network modeling. , 2005, Physical review letters.

[37]  Steven I. Marcus,et al.  Modeling and analysis of stochastic differential equations driven by point processes , 1978, IEEE Trans. Inf. Theory.

[38]  Hirokazu Fujisaka,et al.  Statistical Dynamics Generated by Fluctuations of Local Lyapunov Exponents , 1983 .

[39]  J. Teramae,et al.  Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators. , 2004, Physical review letters.

[40]  A. Winfree.  The geometry of biological time , 1991 .

[41]  Platt,et al.  Characterization of on-off intermittency. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[42]  Peter A Tass,et al.  Desynchronization of coupled electrochemical oscillators with pulse stimulations. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  Yasuhiro Tsubo,et al.  Synchrony of limit-cycle oscillators induced by random external impulses. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  T. Sejnowski,et al.  Reliability of spike timing in neocortical neurons. , 1995, Science.

[45]  Yoji Kawamura,et al.  Noise-induced synchronization and clustering in ensembles of uncoupled limit-cycle oscillators. , 2007, Physical review letters.

[46]  S. Lowen.  The Biophysical Journal , 1960, Nature.

[47]  H. Robinson,et al.  Phase resetting curves and oscillatory stability in interneurons of rat somatosensory cortex. , 2007, Biophysical journal.

[48]  Benner,et al.  On-off intermittency in spin-wave instabilities. , 1995, Physical review letters.

[49]  James R. Gilbert,et al.  Analytical Population Dynamics , 1994 .

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

[51]  Nicolas Fourcaud-Trocmé,et al.  Correlation-induced Synchronization of Oscillations in Olfactory Bulb Neurons , 2022 .

[52]  Peter A. Tass,et al.  Phase Resetting in Medicine and Biology: Stochastic Modelling and Data Analysis , 1999 .