2011/12/26 by James Ing, Ing, James, Sergey Kryzhevich +3
Computer Science · Mathematics · Physics and Astronomy · #37D45 #37G20 #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #math.DS #msc:37D45 #msc:37G20
paper · pdf · doi:10.48550/arxiv.1112.5841
23 pages, 5 figures
openalex publication_date 2011/12/26 · arxiv created 2012/11/02 · arxiv updated 2012/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well-known for vibro-impact systems that the existence of a periodic\nsolution with a low-velocity impact (so-called grazing) may yield complex\nbehavior of the solutions. In this paper we show that unstable periodic motions\nwhich pass near the delimiter without touching it may give birth to chaotic\nbehavior of nearby solutions. We demonstrate that the number of impacts over a\nperiod of forcing varies in a small neighborhood of such periodic motions. This\nallows us to use the technique of symbolic dynamics. It is shown that chaos may\nbe observed in a two-sided neighborhood of grazing and this bifurcation\nmanifests at least two distinct ways to a complex behavior. In the second part\nof the paper we study the robustness of this phenomenon. Particularly, we show\nthat the same effect can be observed in "soft" models of impacts.\n