Transition from homogeneous to inhomogeneous limit cycles: Effect of local filtering in coupled oscillators

Tanmoy Banerjee, Debabrata Biswas, Debarati Ghosh, Biswabibek Bandyopadhyay, Juergen Kurths

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Abstract

We report an interesting symmetry-breaking transition in coupled identical oscillators, namely the continuous transition from homogeneous to inhomogeneous limit cycle oscillations. The observed transition is the oscillatory analog of the Turing-type symmetry-breaking transition from amplitude death (i.e., stable homogeneous steady state) to oscillation death (i.e., stable inhomogeneous steady state). This novel transition occurs in the parametric zone of occurrence of rhythmogenesis and oscillation death as a consequence of the presence of local filtering in the coupling path. We consider paradigmatic oscillators, such as Stuart-Landau and van der Pol oscillators under mean-field coupling with low-pass or all-pass filtered self-feedback and through a rigorous bifurcation analysis we explore the genesis of this transition. Further, we experimentally demonstrate the observed transition, which establishes its robustness in the presence of parameter fluctuations and noise.
Original languageEnglish
Article number042218
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume97
Issue number4
Early online date25 Apr 2018
DOIs
Publication statusPublished - Apr 2018

Keywords

  • nlin.CD
  • nlin.AO
  • physics.app-ph

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