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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