TY - JOUR
T1 - Riddled-like Basin in Two-Dimensional Map for Bouncing Motion of an Inelastic Particle on a Vibrating Board
AU - Fukano, Shohei
AU - Hayase, Yumino
AU - Nakanishi, Hiizu
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2002/9
Y1 - 2002/9
N2 - 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.
AB - 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.
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U2 - 10.1143/JPSJ.71.2075
DO - 10.1143/JPSJ.71.2075
M3 - Article
AN - SCOPUS:0036919898
VL - 71
SP - 2075
EP - 2077
JO - Journal of the Physical Society of Japan
JF - Journal of the Physical Society of Japan
SN - 0031-9015
IS - 9
ER -