Coalescence of the two secondary responses in coupled duffing equations

Ting Yu Lai, Pi Cheng Tung, Yung Chia Hsiao

Research output: Contribution to journalArticlepeer-review


The novel coalescence of the secondary responses for the coupled Duffing equations are observed in this study. Two secondary responses that do not bifurcate from the primary responses merge into one due to saddle-node bifurcation generation within a specific parameter range. The frequency responses of the coupled Duffing equations are calculated using the harmonic balance method while the periodic orbits are detected by the shooting method. The stability of the periodic orbits is determined on utilizing Floquet theory. The parametric continuation algorithm is used to obtain the bifurcation points and bifurcation lines for a Duffing system with two varying parameters. The analytical results demonstrate the novel phenomenon that occurs in the Duffing equations.

Original languageEnglish
Article number1250149
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number6
StatePublished - Jun 2012


  • Duffing equation
  • saddle-node
  • Secondary responses


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