- Virgin, L.N. and Begley, C.J., Grazing bifurcations and basins of attraction in an impact-friction oscillator,
Physica D: Nonlinear Phenomena, vol. 130 no. 1
pp. 43 - 57 [S0167-2789(99)00016-0] .
(last updated on 2007/03/23)
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.