Period-doubling density waves in a chain

Joost H.J. van Opheusden, Theo P. Valkering

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    Abstract

    The authors consider a one-dimensional chain of N+2 identical particles with nearest-neighbour Lennard-Jones interaction and uniform friction. The chain is driven by a prescribed periodic motion of one end particle, with frequency v and 'strength' parameter alpha . The other end particle is held fixed. They demonstrate numerically that there is a region in the alpha -v plane where the chain has a stable state in which a density wave runs to and fro between the two ends of the chain, similarly to a ball bouncing between two walls. More importantly, they observe a period-doubling transition to chaos, for fixed v and increasing alpha , while the localised (solitary wave) character of the motion is preserved
    Original languageEnglish
    Pages (from-to)357
    JournalNonlinearity
    Volume2
    Issue number2
    DOIs
    Publication statusPublished - 1989

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  • Cite this

    van Opheusden, J. H. J., & Valkering, T. P. (1989). Period-doubling density waves in a chain. Nonlinearity, 2(2), 357. https://doi.org/10.1088/0951-7715/2/2/010