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- W2949436314 abstract "We model pacemaker effects of an algebraically localized heterogeneity in a 1 dimensional array of oscillators with nonlocal coupling. We assume the oscillators obey simple phase dynamics and that the array is large enough so that it can be approximated by a continuous nonlocal evolution equation. We concentrate on the case of heterogeneities with positive average and show that steady solutions to the nonlocal problem exist. In particular, we show that these heterogeneities act as a wave source, sending out waves in the far field. This effect is not possible in 3 dimensional systems, such as the complex Ginzburg-Landau equation, where the wavenumber of weak sources decays at infinity. To obtain our results we use a series of isomorphisms to relate the nonlocal problem to the viscous eikonal equation. We then use Fredholm properties of the Laplace operator in Kondratiev spaces to obtain solutions to the eikonal equation, and by extension to the nonlocal problem." @default.
- W2949436314 created "2019-06-27" @default.
- W2949436314 creator A5043409313 @default.
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- W2949436314 date "2014-09-05" @default.
- W2949436314 modified "2023-09-27" @default.
- W2949436314 title "Pacemakers in large arrays of oscillators with nonlocal coupling" @default.
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