Coupled Lorenz oscillators near the Hopf boundary: Multistability, intermingled basins, and quasiriddling

Thierry T. Wontchui, Joseph Y. Effa, H. P.Ekobena Fouda, Sangeeta R. Ujjwal, Ram Ramaswamy

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We investigate the dynamics of coupled identical chaotic Lorenz oscillators just above the subcritical Hopf bifurcation. In the absence of coupling, the motion is on a strange chaotic attractor and the fixed points of the system are all unstable. With the coupling, the unstable fixed points are converted into chaotic attractors, and the system can exhibit a multiplicity of coexisting attractors. Depending on the strength of the coupling, the motion of the individual oscillators can be synchronized (both in and out of phase) or desynchronized and in addition there can be mixed phases. We find that the basins have a complex structure: the state that is asymptotically reached shows extreme sensitivity to initial conditions. The basins of attraction of these different states are characterized using a variety of measures and depending on the strength of the coupling, they are intermingled or quasiriddled.

Original languageEnglish
Article number062203
JournalPhysical Review E
Volume96
Issue number6
DOIs
StatePublished - 11 Dec 2017

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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