Grazing bifurcations in impact oscillators

Wai Chin (1, 2) , Edward Ott (2, 3) , Helena E. Nusse (4) , Celso Grebogi (1, 2, 4)

1 Department of Mathematics
2 Institute for Plasma Research
3 Department of Electrical Engineering
4 Institute for Physical Science and Technology

Impact oscillators demonstrate interesting dynamical features. In particular, new types of bifurca-tions take place as such systems evolve from a nonimpacting to an impacting state (or vice versa), as a system parameter varies smoothly. These bifurcations are called grazing bifurcations. In this paper we analyze the different types of grazing bifurcations that can occur in a simple sinusoidally forced oscilla-tor system in the presence of friction and a hard wall with which the impacts take place. The general picture we obtain exemplifies universal features that are predicted to occur in a wide variety of impact oscillator systems

Domaines: Mathématiques [math]; Sciences de l'ingénieur [physics]; Vibrations [physics.class-ph]

Wai Chin, Edward Ott, Helena E. Nusse, Celso Grebogi. Grazing bifurcations in impact oscillators. Physical Review E , 1994, 50 (6), pp.4427 - 4444. ⟨10.1103/PhysRevE.50.4427⟩. ⟨hal-01386141⟩