Collective phase sensitivity.

The collective phase response to a macroscopic external perturbation of a population of interacting nonlinear elements exhibiting collective oscillations is formulated for the case of globally coupled oscillators. The macroscopic phase sensitivity is derived from the microscopic phase sensitivity of the constituent oscillators by a two-step phase reduction. We apply this result to quantify the stability of the macroscopic common-noise-induced synchronization of two uncoupled populations of oscillators undergoing coherent collective oscillations.

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

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

[3]  S. Strogatz.  From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators , 2000 .

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

[5]  Yoji Kawamura,et al.  Noise-induced turbulence in nonlocally coupled oscillators. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[8]  Monika Sharma,et al.  Chemical oscillations , 2006 .

[9]  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 .

[10]  Hiroshi Kori,et al.  Engineering Complex Dynamical Structures: Sequential Patterns and Desynchronization , 2007, Science.

[11]  A. Mikhailov,et al.  Emergence of Dynamical Order: Synchronization Phenomena in Complex Systems , 2004 .

[12]  J. Kurths,et al.  Synchronization of two interacting populations of oscillators. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  R. Spigler,et al.  The Kuramoto model: A simple paradigm for synchronization phenomena , 2005 .

[14]  G. Kraepelin,et al.  A. T. Winfree, The Geometry of Biological Time (Biomathematics, Vol.8). 530 S., 290 Abb. Berlin‐Heidelberg‐New‐York 1980. Springer‐Verlag. DM 59,50 , 1981 .

[15]  Nicolas Brunel,et al.  Fast Global Oscillations in Networks of Integrate-and-Fire Neurons with Low Firing Rates , 1999, Neural Computation.

[16]  C. Gardiner.  Handbook of Stochastic Methods , 1983 .

[17]  John L Hudson,et al.  Emerging Coherence in a Population of Chemical Oscillators , 2002, Science.