Abstract
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.
Original language | English |
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Article number | 035202 |
Number of pages | 4 |
Journal | Physical Review. E, Statistical, Nonlinear and Soft Matter Physics |
Volume | 67 |
Issue number | 3 |
DOIs | |
Publication status | Published - Mar 2003 |
Keywords
- on-off intermittency
- trajectories
- sets