CNCS Center for Nonlinear and Complex Systems
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Publications [#282516] of Lawrence N. Virgin

Papers Published

  1. Virgin, LN; Begley, CJ, Grazing bifurcations and basins of attraction in an impact-friction oscillator, Physica D: Nonlinear Phenomena, vol. 130 no. 1-2 (1999), pp. 43-57, Elsevier BV, ISSN 0167-2789 [Gateway.cgi], [doi]
    (last updated on 2019/09/18)

    Abstract:
    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.