Discrete breathers in an array of self-excited oscillators: Exact solutions and stability

I. B. Shiroky, O. V. Gendelman

Research output: Contribution to journalArticlepeer-review

Abstract

We consider dynamics of array of coupled self-excited oscillators. The model of Franklin bell is adopted as a mechanism for the self-excitation. The model allows derivation of exact analytic solutions for discrete breathers (DBs) and exploration of their stability in the space of parameters. The DB solutions exist for all frequencies in the attenuation zone but lose stability via Neimark-Sacker bifurcation in the vicinity of the bandgap boundary. Besides the well-known DBs with exponential localization, the considered system possesses novel type of solutions discrete breathers with main frequency in the propagation zone of the chain. In these regimes, the energy irradiation into the chain is balanced by the self excitation. The amplitude of oscillations is maximal at the localization site and then exponentially approaches constant value at infinity. We also derive these solutions in the closed analytic form. They are stable in a narrow region of system parameters bounded by Neimark-Sacker and pitchfork bifurcations.

Original languageEnglish
Article number103112
JournalChaos
Volume26
Issue number10
DOIs
StatePublished - 1 Oct 2016

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Statistical and Nonlinear Physics
  • General Physics and Astronomy
  • Mathematical Physics

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