An Analytical Approach to Codimension-2 Sliding Bifurcations in the Dry-Friction Oscillator

作者：Guardia Marcel^*; Hogan S John; Seara Tere M

来源：SIAM Journal on Applied Dynamical Systems, 2010, 9(3): 769-798.

DOI：10.1137/090766826

• Filippov systems
• periodic orbits
• sliding bifurcations
• codimension-2 points

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., the frequency of the forcing. We prove the existence of infinitely many codimension-2 bifurcation points and focus our attention on two of them: A(1) := (omega(-1), F) = (2, 1/3) and B-1 := (omega(-1), F) = (3, 0). We derive analytic expressions in (omega(-1), F) parameter space for the codimension-1 bifurcation curves that emanate from A(1) and B-1. Our results show excellent agreement with the numerical calculations of Kowalczyk and Piiroinen [Phys. D, 237 (2008), pp. 1053-1073].

• 出版日期2010