Crises in a dissipative bouncing ball model

Andre Livorati*, Iberê L. Caldas, Carl P. Dettmann, Edson D. Leonel

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

14 Citations (Scopus)
297 Downloads (Pure)


The dynamics of a bouncing ball model under the influence of dissipation is investigated by using a two-dimensional nonlinear mapping. When high dissipation is considered, the dynamics evolves to different attractors. The evolution of the basins of the attracting fixed points is characterized, as we vary the control parameters. Crises between the attractors and their boundaries are observed. We found that the multiple attractors are intertwined, and when the boundary crisis between their stable and unstable manifolds occurs, it creates a successive mechanism of destruction for all attractors originated by the sinks. Also, a physical impact crisis is described, an important mechanism in the reduction of the number of attractors.

Original languageEnglish
Pages (from-to)2830-2838
Number of pages9
JournalPhysics Letters A
Issue number43-44
Early online date14 Sept 2015
Publication statusPublished - 6 Nov 2015

Bibliographical note

Date of Acceptance: 10/09/2015


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