Characterization in bi-parameter space of a non-ideal oscillator

S. L. T. de Souza, A. M. Batista, M. S. Baptista, I. L. Caldas, J. M. Balthazar

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)
12 Downloads (Pure)


We investigate the dynamical behavior of a non-ideal Duffing oscillator, a system composed of a mass–spring–pendulum driven by a DC motor with limited power supply. To identify new features on Duffing oscillator parameter space due to the limited power supply, we provide an extensive numerical characterization in the bi-parameter space by using Lyapunov exponents. Following this procedure, we identify remarkable new organized distribution of periodic windows, the ones known as Arnold tongues and also shrimp-shaped structures. In addition, we also identify intertwined basins of attraction for coexisting multiple attractors connected with tongues.
Original languageEnglish
Pages (from-to)224-231
Number of pages8
JournalPhysica. A, Statistical Mechanics and its Applications
Early online date21 Sept 2016
Publication statusPublished - 15 Jan 2017

Bibliographical note

The authors thank scientific agencies CAPES, CNPq (112952/2015-1), and FAPESP (2011/ 19269-11). M. S. Baptista also thanks EPSRC (EP/I03 2606/1).


  • chaos
  • Arnold tongues
  • shrimp-shaped structures
  • coupled oscillators


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