Unstable recurrent patterns in Kuramoto-Sivashinsky dynamics.
نویسندگان
چکیده
We undertake an exploration of recurrent patterns in the antisymmetric subspace of the one-dimensional Kuramoto-Sivashinsky system. For a small but already rather "turbulent" system, the long-time dynamics takes place on a low-dimensional invariant manifold. A set of equilibria offers a coarse geometrical partition of this manifold. The Newton descent method enables us to determine numerically a large number of unstable spatiotemporally periodic solutions. The attracting set appears surprisingly thin-its backbone consists of several Smale horseshoe repellers, well approximated by intrinsic local one-dimensional return maps, each with an approximate symbolic dynamics. The dynamics appears decomposable into chaotic dynamics within such local repellers, interspersed by rapid jumps between them.
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عنوان ژورنال:
- Physical review. E, Statistical, nonlinear, and soft matter physics
دوره 78 2 Pt 2 شماره
صفحات -
تاریخ انتشار 2008