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 codimens...
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].
Citació
Martínez-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.
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