Validity of numerical trajectories in the synchronization transition of complex systems

Details Validity of numerical trajectories in the synchronization transition of complex systems Validity of numerical trajectories in the synchronization transition of complex systems

2003-10-07

arxiv.org/abs/nlin/0310004v1

Nonlinear Sciences

Chaotic Dynamics

4 pages, 4 figures

Scientific paper

10.1103/PhysRevE.68.067204

We investigate the relationship between the loss of synchronization and the onset of shadowing breakdown {\it via} unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly non-hyperbolic behavior, the system undergoes on-off intermittency with respect to the synchronization state. There are potentially severe consequences of these facts on the validity of the computer-generated trajectories obtained from dynamical systems whose synchronization manifolds share the same non-hyperbolic properties.

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