Estimation of chaotic thresholds for the recently proposed rotating pendulum

N. Han, Q. J. Cao*, M. Wiercigroch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


In this paper, we investigate the nonlinear behavior of the recently proposed rotating pendulum which is a cylindrically nonlinear system with irrational type having smooth and discontinuous characteristics depending on the value of a smoothness parameter. We introduce a cylindrical approximate system whose analytical solutions can be obtained successfully to reflect the nature of the original system without the barrier of irrationalities. Furthermore, Melnikov method is employed to detect the chaotic thresholds for the homoclinic orbits of the second-type, a pair of homoclinic orbits of the first and second-type and the double heteroclinic orbits under the perturbation of viscous damping and external harmonic forcing within the smooth regime. Numerical simulations show the efficiency of the proposed method and the results presented herein this paper demonstrate the predicated chaotic attractors of pendulum-type, SD-type and their mixture depending on the coupling of the nonlinearities.

Original languageEnglish
Article number1350074
Pages (from-to)1-22
Number of pages22
JournalInternational Journal of Bifurcation and Chaos
Issue number4
Publication statusPublished - Apr 2013


  • Chaotic thresholds
  • Irrational nonlinearity
  • Rotating pendulum
  • SD oscillator
  • Singular closed orbits


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