Crises in a dissipative Bouncing ball model
Abstract
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 occur, it creates a successive mechanism of destruction for all attractors originated by the sinks. Also, an impact physical crises is setup, and it may be useful as a mechanism to reduce the number of attractors in the system.
Cite
@article{arxiv.1409.8279,
title = {Crises in a dissipative Bouncing ball model},
author = {André L. P. Livorati and Iberê L. Caldas and Carl P. Dettmann and Edson D. Leonel},
journal= {arXiv preprint arXiv:1409.8279},
year = {2015}
}