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Mathematical Problems in Engineering
Volume 2009, Article ID 290356, 11 pages
Research Article

Multistability and Self-Similarity in the Parameter-Space of a Vibro-Impact System

1Universidade Federal de São João del-Rei, Campus Alto Paraopeba, Km 7 Rodovia MG 443, 36420-000 Ouro Branco, Minas Gerais, Brazil
2Instituto de Física, Universidade de São Paulo, 05315-970 São Paulo, Brazil
3Departamento de Física, Universidade Federal do Paraná, 81531-990 Curitiba, Paraná, Brazil

Received 22 April 2009; Accepted 23 June 2009

Academic Editor: Edson Denis Leonel

Copyright © 2009 Silvio L. T. de Souza et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The dynamics of a dissipative vibro-impact system called impact-pair is investigated. This system is similar to Fermi-Ulam accelerator model and consists of an oscillating one-dimensional box containing a point mass moving freely between successive inelastic collisions with the rigid walls of the box. In our numerical simulations, we observed multistable regimes, for which the corresponding basins of attraction present a quite complicated structure with smooth boundary. In addition, we characterize the system in a two-dimensional parameter space by using the largest Lyapunov exponents, identifying self-similar periodic sets.