Statistics of shadowing time in nonhyperbolic chaotic systems with unstable dimension variability
Abstract
Severe obstruction to shadowing of computergenerated trajectories can occur in nonhyperbolic chaotic systems with unstable dimension variability. That is, when the dimension of the unstable eigenspace changes along a trajectory in the invariant set, no true trajectory of reasonable length can be found to exist near any numerically generated trajectory. An important quantity characterizing the shadowability of numerical trajectories is the shadowing time, which measures for how long a trajectory remains valid. This time depends sensitively on initial condition. Here we show that 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 system details but the smalltime algebraic behavior appears to be universal. We describe the computational procedure for computing the shadowing time and give a physical analysis for the observed scaling behaviors.
 Publication:

Physical Review E
 Pub Date:
 January 2004
 DOI:
 10.1103/PhysRevE.69.016213
 Bibcode:
 2004PhRvE..69a6213D
 Keywords:

 05.45.a;
 05.40.a;
 Nonlinear dynamics and chaos;
 Fluctuation phenomena random processes noise and Brownian motion