Universal and nonuniversal features in shadowing dynamics of nonhyperbolic chaotic systems with unstable-dimension variability

Y H Do, Ying-Cheng Lai, Z H Liu, E J Kostelich

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5 Citations (Scopus)


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 languageEnglish
Article number035202
Number of pages4
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number3
Publication statusPublished - Mar 2003


  • on-off intermittency
  • trajectories
  • sets

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