Fast-slow analysis for parametrically and externally excited systems with two slow rationally related excitation frequencies

Xiujing Han*, Qinsheng Bi, Peng Ji, Juergen Kurths

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

49 Citations (Scopus)


We present a general method for analyzing mixed-mode oscillations (MMOs) in parametrically and externally excited systems with two low excitation frequencies (PEESTLEFs) for the case of arbitrary m:n relation between the slow frequencies of excitations. The validity of the approach has been demonstrated using the equations of Duffing and van der Pol, separately. Our study shows that, by introducing a slow variable and finding the relation between the slow variable and the slow excitations, PEESTLEFs can be transformed into a fast-slow form with a single slow variable and therefore MMOs observed in PEESTLEFs can be understood by the classical machinery of fast subsystem analysis of the transformed fast-slow system.

Original languageEnglish
Article number012911
Number of pages12
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number1
Publication statusPublished - 15 Jul 2015


  • mixed-mode oscillations
  • HOPF-bifurcation
  • catalyst deactivation
  • passage
  • modulation
  • dynamics
  • patterns
  • period
  • chaos
  • weak

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