Crises in a dissipative Bouncing ball model

TL;DR

This paper studies the complex dynamics and crises in a dissipative bouncing ball model, revealing how high dissipation leads to multiple intertwined attractors and their sudden destruction through boundary crises.

Contribution

It introduces a detailed analysis of attractor basins, crises, and a physical impact crisis mechanism in a dissipative bouncing ball system, highlighting new dynamical behaviors.

Findings

Multiple attractors are intertwined under high dissipation.

Boundary crises cause sudden destruction of attractors.

Impact crises can reduce the number of attractors.

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.