Journal of Statistical Physics

, Volume 60, Issue 1, pp 245-262

First online:

Amplitude death in an array of limit-cycle oscillators

  • Renato E. MirolloAffiliated withDepartment of Mathematics, Boston College
  • , Steven H. StrogatzAffiliated withDepartment of Mathematics, Massachusetts Institute of Technology

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We analyze a large system of limit-cycle oscillators with mean-field coupling and randomly distributed natural frequencies. We prove that when the coupling is sufficiently strong and the distribution of frequencies has sufficiently large variance, the system undergoes “amplitude death”-the oscillators pull each other off their limit cycles and into the origin, which in this case is astable equilibrium point for the coupled system. We determine the region in couplingvariance space for which amplitude death is stable, and present the first proof that the infinite system provides an accurate picture of amplitude death in the large but finite system.

Key words

Nonlinear oscillator bifurcation phase transition mean-field model self-synchronization collective phenomena