Collective phase description of globally coupled excitable elements

Details Collective phase description of globally coupled excitable elements Collective phase description of globally coupled excitable elements

2011-10-05

arxiv.org/abs/1110.0914v1

Phys. Rev. E 84, 046211 (2011)

Nonlinear Sciences

Adaptation and Self-Organizing Systems

18 pages, 6 figures

Scientific paper

10.1103/PhysRevE.84.046211

We develop a theory of collective phase description for globally coupled noisy excitable elements exhibiting macroscopic oscillations. Collective phase equations describing macroscopic rhythms of the system are derived from Langevin-type equations of globally coupled active rotators via a nonlinear Fokker-Planck equation. The theory is an extension of the conventional phase reduction method for ordinary limit cycles to limit-cycle solutions in infinite-dimensional dynamical systems, such as the time-periodic solutions to nonlinear Fokker-Planck equations representing macroscopic rhythms. We demonstrate that the type of the collective phase sensitivity function near the onset of collective oscillations crucially depends on the type of the bifurcation, namely, it is type-I for the saddle-node bifurcation and type-II for the Hopf bifurcation.

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