Validity of numerical trajectories in the synchronization transition of complex systems

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.

arXiv comment4 pages, 4 figures

References in corpus (1)

• Unstable dimension variability and synchronization of chaotic systems

Cited by in corpus (6)

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• Synchronization time in a hyperbolic dynamical system with long-range interactions
• Violation of hyperbolicity via unstable dimension variability in a chain with local hyperbolic chaotic attractors