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Validity of numerical trajectories in the synchronization transition of complex systems

R. L. Viana·C. Grebogi·S. E. de S. Pinto·S. R. Lopes·A. M. Batista·J. Kurths
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Abstract

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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R. L. Viana, C. Grebogi, S. E. de S. Pinto, S. R. Lopes, A. M. Batista, J. Kurths. 2003-10-07. Validity of numerical trajectories in the synchronization transition of complex systems. https://doi.org/10.1103/physreve.68.067204

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