Smale Horseshoe and Grazing Bifurcation in Impact Systems

TL;DR

This paper investigates how parameter changes in impact systems can lead to complex chaotic behavior, specifically through bifurcations that increase impacts in periodic solutions, revealing hyperbolic chaotic sets.

Contribution

It introduces a novel analysis of bifurcations in impact systems, linking impact number increases to the emergence of hyperbolic chaos.

Findings

Variation of parameters increases impact count in periodic solutions

Hyperbolic chaotic invariant sets emerge during bifurcations

Impact systems exhibit complex chaotic dynamics

Abstract

Bifurcations of dynamical systems, described by a second order differential equations and by an impact condition are studied. It is shown that the variation of parameters when the number of impacts of a periodic solution increases, leads to the occurrence of a hyperbolic chaotic invariant set.