An analytical approach to codimension-2 sliding bifurcations in the dry friction oscillator
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In this paper, we analytically consider sliding bifurcations of periodic orbits in the dry-friction oscillator. The system depends on two parameters: F, which corresponds to the intensity of the friction, and ω, the frequency of the forcing. We prove the existence of infinitely many codimension-2 bifurcation points and focus our attention on two of them: A1 := (ω −1, F) = (2, 1/3) and B1 := (ω −1, F) = (3, 0). We derive analytic expressions in (ω −1, F) parameter space for the codimension-1 bifurcation curves that emanate from A1 and B1. Our results show excellent agreement with the numerical calculations of Kowalczyk and Piiroinen [Phys. D, 237 (2008), pp. 1053–1073].
CitationMartínez-Seara, M.; Guardia, M.; Hogan, J. An analytical approach to codimension-2 sliding bifurcations in the dry friction oscillator. "SIAM journal on applied dynamical systems", 2010, vol. 9, núm. 3, p. 769-798.