Unstable dimension variability and synchronization of chaotic systems

Abstract

An aspect of the synchronization dynamics is investigated in this work. We argue analytically and confirm numerically that the chaotic dynamics on the synchronization manifold exhibits unstable dimension variability. Unstable dimension variability is a cause of severe modeling difficulty for physical phenomena, since trajectories obtained from the mathematical model may not be related to trajectories of the actual system. We present and example of unstable dimension variability occurring in a system of two coupled chaotic maps, considering the dynamics in the synchronization manifold and its corresponding transversal direction, where a tongue-like structure is formed. The unstable dimension variability is revealed in the statistical distribution of the finite-time transversal Lyapunov exponent, having both negative and positive values.

25 pages, 8 figures, RevTex format

References in corpus (1)

• Characteristic distributions of finite-time Lyapunov exponents

Cited by in corpus (4)

• Validity of numerical trajectories in the synchronization transition of complex systems
• Super persistent transient in a master-slave configuration with Colpitts oscillators
• Violation of hyperbolicity via unstable dimension variability in a chain with local hyperbolic chaotic attractors
• Unstable dimension variability, heterodimensional cycles, and blenders in the border-collision normal form