Novel smooth and discontinuous oscillator with strong irrational nonlinearities

Han YanWei, Qingjie Cao, Chen YuShu, Marian Wiercigroch

Research output: Contribution to journalArticlepeer-review

40 Citations (Scopus)


In this paper, we propose a novel nonlinear oscillator with strong irrational nonlinearities having smooth and discontinuous characteristics depending on the values of a smoothness parameter. The oscillator is similar to the SD oscillator, originally introduced in Phys Rev E 69(2006). The equilibrium stability and the complex bifurcations of the unperturbed system are investigated. The bifurcation sets of the equilibria in parameter space are constructed to demonstrate transitions in the multiple well dynamics for both smooth and discontinuous regimes. The Melnikov method is employed to obtain the analytical criteria of chaotic thresholds for the singular closed orbits of homoclinic, homo-heteroclinic, cuspidal heteroclinic and tangent homoclinic orbits of the perturbed system.
Original languageEnglish
Pages (from-to)1832-1843
Number of pages12
JournalScience China Physics, Mechanics & Astronomy
Issue number10
Publication statusPublished - Oct 2012


  • irrational nonlinearity
  • multiple well dynamics
  • singular closed orbits
  • Melnkinov method


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