Computational modeling of diffusive dynamics in a bouncer system with an irregular surface

The horizontal dynamics of a bouncing ball interacting with an irregular surface are investigated and are found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation entropy. The probability density function associated with the particle positions evolves to a Gaussian distribution, and the second moment follows a power-law dependence on time, indicative of diffusive behavior. The results emphasize that deterministic systems with complex geometries or nonlinearities can generate behavior that is statistically indistinguishable from random. Several problems are suggested to extend the analysis.