Some dynamical properties of a classical dissipative bouncing ball model with two nonlinearities - Oliveira, Diego F.M.; Leonel, Edson D. [UNESP] (Elsevier, 2013)
Some dynamical properties for a bouncing ball model are studied. We show that when dissipation is introduced the structure of the phase space is changed and attractors appear. Increasing the amount of dissipation, the edges of the basins of attraction of an attracting fixed point touch the chaotic attractor. Consequently the chaotic attractor and its basin of attraction are destroyed given place to a transient described by a power law with exponent -2. The parameter-space is also studied and we show that it presents a rich structure with infinite self-similar structures of shrimp-shape. © 2013 Elsevier B.V. All rights reserved.
Keywords: Boundary crisis; Chaos; Fermi-map; Basin of attraction; Basins of attraction; Bouncing balls; Chaotic attractors; Dynamical properties; Fixed points; Parameter spaces; Phase spaces; Rich structure; Self-similar; Chaos theory; Physics; Phase space methods