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The instability of chaotic synchronization in coupled Lorenz systems: from the Hopf to the Co-dimension two bifurcation

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  • J. Yang
  • M. Zhang

Abstract

We investigate the Hopf bifurcation of the synchronous chaos in coupled Lorenz oscillators. We find that the system undergoes a phase transition along the Hopf instability of the synchronous chaos. The phase transition makes the traveling wave component with the phase difference φ(i)-φ(i+1)=2π/N between adjacent sites unstable. The phase transition also plays a role to relate the Hopf bifurcation with the co-dimension two bifurcation of the synchronous chaos. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005

Suggested Citation

  • J. Yang & M. Zhang, 2005. "The instability of chaotic synchronization in coupled Lorenz systems: from the Hopf to the Co-dimension two bifurcation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 47(2), pages 251-254, September.
    • Handle: RePEc:spr:eurphb:v:47:y:2005:i:2:p:251-254
    DOI: 10.1140/epjb/e2005-00315-0
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