Universal and nonuniversal features in shadowing dynamics of nonhyperbolic chaotic systems with unstable-dimension variability.
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.
Do
Younghae
Y
Department of Mathematics and Statistics, Arizona State University, Tempe 85287, USA.
Lai
Ying-Cheng
YC
Liu
Zonghua
Z
Kostelich
Eric J
EJ