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- W1998483406 abstract "We study oscillator chains of the form ${stackrel{ifmmode dot{}else .{}fi{}}{ensuremath{phi}}}_{k}={ensuremath{omega}}_{k}+K[ensuremath{Gamma}({ensuremath{phi}}_{kensuremath{-}1}ensuremath{-}{ensuremath{phi}}_{k})+ensuremath{Gamma}({ensuremath{phi}}_{k+1}ensuremath{-}{ensuremath{phi}}_{k})]$, where ${ensuremath{phi}}_{k}∊[0,2ensuremath{pi})$ is the phase of oscillator $k$. In the thermodynamic limit where the number of oscillators goes to infinity, for suitable choices of $ensuremath{Gamma}(x)$, we prove that there is a critical coupling strength ${K}_{c}$, above which a stable frequency-entrained state exists, but below which the probability is zero to have such a state. It is assumed that the natural frequencies are random with finite bandwidth. A crucial condition on $ensuremath{Gamma}(x)$ is that it is nonodd, i.e., $ensuremath{mid}ensuremath{Gamma}(x)+ensuremath{Gamma}(ensuremath{-}x)ensuremath{mid}ensuremath{ne}0$. The interest in the results comes from the fact that any chain of limit-cycle oscillators can be described by equations of the above form in the limits of weak coupling and narrow distribution of natural frequencies." @default.
- W1998483406 created "2016-06-24" @default.
- W1998483406 creator A5065668283 @default.
- W1998483406 date "2004-07-28" @default.
- W1998483406 modified "2023-10-02" @default.
- W1998483406 title "Frequency entrainment in long chains of oscillators with random natural frequencies in the weak coupling limit" @default.
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- W1998483406 doi "https://doi.org/10.1103/physreve.70.016120" @default.
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