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arXiv · 0804.2474

Unstable recurrent patterns in Kuramoto-Sivashinsky dynamics

Yueheng Lan·Predrag Cvitanovic
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Abstract

We undertake a systematic exploration of recurrent patterns in a 1-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. A variational method enables us to determine numerically a large number of unstable spatiotemporally periodic solutions. The attracting set appears surprisingly thin - its backbone are several Smale horseshoe repellers, well approximated by intrinsic local 1-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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Yueheng Lan, Predrag Cvitanovic. 2008-04-15. Unstable recurrent patterns in Kuramoto-Sivashinsky dynamics. https://doi.org/10.1103/physreve.78.026208

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