Transport and dynamical properties for a bouncing ball model with regular and stochastic perturbations

Diogo Ricardo da Costa*, Carl P. Dettmann, Edson D. Leonel

*Corresponding author for this work

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

11 Citations (Scopus)


Some statistical properties related to the diffusion in energy for an ensemble of classical particles in a bouncing ball model are studied. The particles are confined to bounce between two rigid walls. One of them is fixed while the other oscillates. The dynamics is described by a two dimensional nonlinear map for the velocity of the particle and time at the instant of the collision. Two different types of change of momentum are considered: (i) periodic due to a sine function and (ii) stochastic. For elastic collisions case (i) leads to finite diffusion in energy while (ii) produces unlimited diffusion. On the other hand, inelastic collisions yield either (i) and (ii) to have limited diffusion. Scaling arguments are used to investigate some properties of the transport coefficient in the chaotic low energy region. Scaling exponents are also obtained for both conservative and dissipative case for cases (i) and (ii). We show that the parameter space has complicated structures either in Lyapunov as well as period coordinates. When stochasticity is introduced in the dynamics, we observed the destruction of the parameter space structures.

Original languageEnglish
Pages (from-to)871-881
Number of pages11
JournalCommunications in Nonlinear Science and Numerical Simulation
Issue number3
Publication statusPublished - 1 Jan 2015


  • Bouncing ball
  • Chaos
  • Parameter space
  • Stochastic
  • Transport properties


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