Crises in a dissipative bouncing ball model

Author(s)

Livorati, Andre L. P. ^{[1, 2, 3]} ; Caldas, Ibere L. ^[3] ; Dettmann, Carl P. ^[2] ; Leonel, Edson D. ^[1]

Affiliation

^[1] Univ Estadual Paulista, UNESP, Dept Fis, BR-13506900 Rio Claro, SP - Brazil

^[2] Univ Bristol, Sch Math, Bristol BS8 1TW, Avon - England

^[3] Univ Sao Paulo, IFUSP, Inst Fis, BR-05314970 Sao Paulo, SP - Brazil

• Document type: Journal article
• Source: Physics Letters A; v. 379, n. 43-44, p. 2830-2838, NOV 6 2015.
• Web of Science Citations: 10

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 occurs, it creates a successive mechanism of destruction for all attractors originated by the sinks. Also, a physical impact crisis is described, an important mechanism in the reduction of the number of attractors. (C) 2015 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 12/23688-5 - Exponents and scaling laws, phase transitions and transport properties of time dependent systems
• Grantee: Edson Denis Leonel
• Support Opportunities: Regular Research Grants
• FAPESP's process: 14/25316-3 - Investigation of transport and diffusion properties of particles using escape formalism for time-dependent systems
• Grantee: André Luís Prando Livorati
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 11/19296-1 - Nonlinear dynamics
• Grantee: Iberê Luiz Caldas
• Support Opportunities: Research Projects - Thematic Grants