TY - JOUR
T1 - Universal and nonuniversal features in shadowing dynamics of nonhyperbolic chaotic systems with unstable-dimension variability
AU - Do, Younghae
AU - Lai, Ying-Cheng
AU - Liu, Zonghua
AU - Kostelich, Eric
PY - 2003
Y1 - 2003
N2 - An important quantity characterizing the shadowability of computer-generated trajectories in nonhyperbolic chaotic system is the shadowing time, which measures for how long a numerical trajectory remains valid. This time depends sensitively on an initial condition. Here, we show that for nonhyperbolic systems with unstable-dimension variability, the probability distribution of the shadowing time contains two distinct scaling behaviors: an algebraic scaling for short times and an exponential scaling for long times. The exponential behavior depends on the system details but the small-time algebraic behavior appears to be universal.
AB - An important quantity characterizing the shadowability of computer-generated trajectories in nonhyperbolic chaotic system is the shadowing time, which measures for how long a numerical trajectory remains valid. This time depends sensitively on an initial condition. Here, we show that for nonhyperbolic systems with unstable-dimension variability, the probability distribution of the shadowing time contains two distinct scaling behaviors: an algebraic scaling for short times and an exponential scaling for long times. The exponential behavior depends on the system details but the small-time algebraic behavior appears to be universal.
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U2 - 10.1103/PhysRevE.67.035202
DO - 10.1103/PhysRevE.67.035202
M3 - Article
AN - SCOPUS:85037252429
SN - 1063-651X
VL - 67
SP - 4
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 3
ER -