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Generalized synchronization and coherent structures in spatially extended systems

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  • Basnarkov, Lasko
  • Duane, Gregory S.
  • Kocarev, Ljupco

Abstract

We study the synchronization of a coupled pair of one-dimensional Kuramoto–Sivashinsky systems, with equations augmented by a third-space-derivative term. With two different values of a system parameter, the two systems synchronize in the generalized sense. The phenomenon persists even in the extreme case when one of the equations is missing the extra term. Master–slave synchronization error is small, so the generalized synchronization relationship is useful for predicting the state of the master from that of the slave, or conversely, for controlling the slave. The spatial density of coupling points required to bring about generalized synchronization appears to be related to the wavelength of traveling wave solutions, and more generally to the width of coherent structures in the separate systems.

Suggested Citation

  • Basnarkov, Lasko & Duane, Gregory S. & Kocarev, Ljupco, 2014. "Generalized synchronization and coherent structures in spatially extended systems," Chaos, Solitons & Fractals, Elsevier, vol. 59(C), pages 35-41.
    • Handle: RePEc:eee:chsofr:v:59:y:2014:i:c:p:35-41
    DOI: 10.1016/j.chaos.2013.11.007
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    1. Polterovich, Victor & Popov, Vladimir, 2006. "Эволюционная Теория Экономической Политики: Часть I: Опыт Быстрого Развития [An Evolutionary Theory of Economic Policy: Part I: The Experience of Fast Development]," MPRA Paper 22168, University Library of Munich, Germany.
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    1. Suresh, R. & Senthilkumar, D.V. & Lakshmanan, M. & Kurths, J., 2016. "Emergence of a common generalized synchronization manifold in network motifs of structurally different time-delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 235-245.

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