Amplitude death in an array of limit-cycle oscillators. (English) Zbl 1086.34525
Summary: 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 a stable equilibrium point for the coupled system. We determine the region in coupling variance 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.
MSC:
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
| 37C55 | Periodic and quasi-periodic flows and diffeomorphisms |
| 34C25 | Periodic solutions to ordinary differential equations |
| 82C44 | Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics |
Keywords:
Nonlinear oscillator; bifurcation; phase transition; mean-field model; self-synchronization; collective phenomenaReferences:
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