Crises in a non-conservative bouncer model

The dynamics of a bouncing ball model under the influence of dissipation is investigated by using a two dimensional nonlinear mapping. The dynamics can be basically described as a free particle that collides with a vibrating plate under the influence of a constant gravitational field. The dissipation is introduced via a restitution coefficient between the vibration platform and the free particle. The perturbation parameter is set as a ratio between accelerations of the particle and the moving platform. For low dissipation regime, the root mean square velocity of the particle grows for short times, pass through a crossover and then bend towards a stationary state. This behaviour is characterized by scaling laws. 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, a physical impact crises is described, an important mechanism in the reduction of the number of attractors.