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, and Ram Ramaswamy
Phys. Rev. E 96, 062203 – Published 11 December 2017

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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
6 More
  • Received 19 September 2017

DOI:https://doi.org/10.1103/PhysRevE.96.062203

©2017 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear Dynamics

Authors & Affiliations

Thierry T. Wontchui1,2, Joseph Y. Effa1, H. P. Ekobena Fouda3, Sangeeta R. Ujjwal4, and Ram Ramaswamy2

  • 1Department of Physics, Faculty of Science, The University of Ngaoundéré, P.O. Box 454 Ngaoundéré, Cameroon
  • 2School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
  • 3Laboratoire d'Analyses, Simulations et Essais, IUT, The University of Ngaoundéré, Cameroon, P.O. Box 455 Ngaoundéré, Cameroon
  • 4Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, 84990, Israel

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 96, Iss. 6 — December 2017

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×