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

Memory in random bouncing ball dynamics

“…In most cases, the BB model has been studied with a harmonic vertical motion of the plate (see, e.g., [12][13][14][15][16][17]). The BB model with random vibrations of the plate, in spite of its practical relevance to real systems and of the qualitatively new dynamic regimes it offers, has been much less investigated ( [18,19] for BB or [20,21] for a modified BB model in which the ball is confined between two walls or when the ball is attached to a fixed wall through an elastic spring [22]). In all these studies, the model was treated using a non-linear mapping (Poincaré map) for which the ball velocity v n just after the n-th impact is related to v n−1 and to the plate velocity w n at the instant of the n-th impact.…”