Title: An analytical approach to codimension-2 sliding 
bifurcations in
the dry friction oscillator

Authors: M. Guardia, S. J. Hogan, T. M. Seara
July 31, 2009

Abstract:
In this paper, we consider analytically 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 $\omega$, the frequency of the forcing. We 
prove the existence of infinitely many codimension-2
bifurcation points and we 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 $B_1$. We 
show excellent agreement with the numerical
calculations of Kowalczyk and Piiroinen [KP08].

Keywords: Filippov systems, periodic orbits, sliding 
bifurcations, codimension-2 points.

AMS classification scheme numbers: 37G15, 34A36, 34C25, 
34C23.