Riddled-like Basin in Two-Dimensional Map for Bouncing Motion of an Inelastic Particle on a Vibrating Board

Shohei Fukano, Yumino Hayase, Hiizu Nakanishi

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Abstract

Motivated by bouncing motion of an inelastic particle on a vibrating board, a simple two-dimensional map is constructed and its behavior is studied numerically. In addition to the typical route to chaos through a periodic doubling bifurcation, we found peculiar behavior in the parameter region where two stable periodic attractors coexist. A typical orbit in the region goes through chaotic motion for an extended transient period before it converges into one of the two periodic attractors. The basin structure in this parameter region is almost riddling and the fractal dimension of the basin boundary is close to two, i.e., the dimension of the phase space.

Original languageEnglish
Pages (from-to)2075-2077
Number of pages3
Journaljournal of the physical society of japan
Volume71
Issue number9
DOIs
Publication statusPublished - Sep 1 2002

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All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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