Unbounded sequences of stable limit cycles in the delayed Duffing equation: an exact analysis

Si Mohamed Sah*, Bernold Fiedler, B. Shayak, Richard H. Rand

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

The delayed Duffing equation x¨(t)+x(t−T)+x3(t)=0 is shown to possess an infinite and unbounded sequence of rapidly oscillating, asymptotically stable periodic solutions, for fixed delays such that T2<32π2. In contrast to several previous works which involved approximate solutions, the treatment here is exact.
Original languageEnglish
JournalNonlinear Dynamics
Volume103
Pages (from-to)503–515
ISSN0924-090X
DOIs
Publication statusPublished - 2021

Keywords

  • Delayed Duffing oscillator
  • Limit cycle
  • Exact analysis
  • Jacobi elliptic function

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