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Grazing bifurcations and basins of attraction in an impact-friction oscillator

Publication ,  Journal Article
Virgin, LN; Begley, CJ
Published in: Physica D: Nonlinear Phenomena
June 1, 1999

This paper describes some interesting global dynamic behavior in the response of a double-sided, harmonically-forced, impact oscillator including the influence of Coulomb damping. The system under study is modeled as piecewise linear in both its force-deflection and force-velocity characteristics. Grazing bifurcations caused by this latter effect are a new feature. The paper has two distinct but related foci. First, the study of basins of attraction provides information regarding the complete solution set for the system, given a specific set of parameters. Second, grazing bifurcations represent the primary source of sudden change in qualitative behavior as a system parameter is varied. The numerical technique of cell-to-cell mapping provides a useful insight into the relation between these two. Thus, both local and global issues are addressed - indeed it is the interplay of periodic attractors and their basins of attraction that dominates bifurcational behavior. ©1999 Elsevier Science B.V. All rights reserved.

Duke Scholars

Published In

Physica D: Nonlinear Phenomena

DOI

ISSN

0167-2789

Publication Date

June 1, 1999

Volume

130

Issue

1-2

Start / End Page

43 / 57

Related Subject Headings

  • Fluids & Plasmas
  • 4903 Numerical and computational mathematics
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

Citation

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Virgin, L. N., & Begley, C. J. (1999). Grazing bifurcations and basins of attraction in an impact-friction oscillator. Physica D: Nonlinear Phenomena, 130(1–2), 43–57. https://doi.org/10.1016/S0167-2789(99)00016-0
Virgin, L. N., and C. J. Begley. “Grazing bifurcations and basins of attraction in an impact-friction oscillator.” Physica D: Nonlinear Phenomena 130, no. 1–2 (June 1, 1999): 43–57. https://doi.org/10.1016/S0167-2789(99)00016-0.
Virgin LN, Begley CJ. Grazing bifurcations and basins of attraction in an impact-friction oscillator. Physica D: Nonlinear Phenomena. 1999 Jun 1;130(1–2):43–57.
Virgin, L. N., and C. J. Begley. “Grazing bifurcations and basins of attraction in an impact-friction oscillator.” Physica D: Nonlinear Phenomena, vol. 130, no. 1–2, June 1999, pp. 43–57. Scopus, doi:10.1016/S0167-2789(99)00016-0.
Virgin LN, Begley CJ. Grazing bifurcations and basins of attraction in an impact-friction oscillator. Physica D: Nonlinear Phenomena. 1999 Jun 1;130(1–2):43–57.
Journal cover image

Published In

Physica D: Nonlinear Phenomena

DOI

ISSN

0167-2789

Publication Date

June 1, 1999

Volume

130

Issue

1-2

Start / End Page

43 / 57

Related Subject Headings

  • Fluids & Plasmas
  • 4903 Numerical and computational mathematics
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics