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Differential Equations

, Volume 54, Issue 9, pp 1266–1270 | Cite as

Traveling Waves and Space-Time Chaos in the Kuramoto–Sivashinsky Equation

  • N. A. Magnitskii
Short Communications

Abstract

The transition to space-time chaos in the Kuramoto–Sivashinsky equation through cascades of traveling wave bifurcations in accordance with the Feigenbaum–Sharkovskii–Magnitskii universal bifurcation scenario is analyzed analytically and numerically. It is proved that the bifurcation parameter is the traveling wave propagation velocity along the spatial axis, which does not explicitly occur in the original equation.

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References

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Federal Research Center “Computer Science and Control” of the Russian Academy of SciencesMoscowRussia
  2. 2.Lomonosov Moscow State UniversityMoscowRussia

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