1999/11/19 by Ricardo L. Viana, Celso Grebogi · 2 citations
Computer Science · Physics and Astronomy · #Chaos control and synchronization #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #chao-dyn #nlin.CD
paper · pdf · doi:10.1103/physreve.62.462
25 pages, 8 figures, RevTex format
arxiv created 1999/11/19 · openalex publication_date 2000/07/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The nonhyperbolic structure of synchronization dynamics is investigated in this work. We argue analytically and confirm numerically that the chaotic dynamics on the synchronization manifold exhibits an unstable dimension variability, which is an extreme form of nonhyperbolicity. We analyze the dynamics in the synchronization manifold and in its transversal direction, where a tonguelike structure is formed, through a system of two coupled chaotic maps. The unstable dimension variability is revealed in the statistical distribution of the finite-time transversal Lyapunov exponent, having both negative and positive values. We also point out that unstable dimension variability is a cause of severe modeling difficulty.