TY  - JOUR
A1  - Vasconcelos, D. B.
A1  - Lopes, S. R.
A1  - Viana, R. L.
A1  - Kurths, Jürgen
T1  - Spatial recurrence plots
N2  - We propose an extension of the recurrence plot concept to perform quantitative analyzes of roughness and disorder of spatial patterns at a fixed time. We introduce spatial recurrence plots (SRPs) as a graphical representation of the pointwise correlation matrix, in terms of a two-dimensional spatial return plot. This technique is applied to the study of complex patterns generated by coupled map lattices, which are characterized by measures of complexity based on SRPs. We show that the complexity measures we propose for SRPs provide a systematic way of investigating the distribution of spatially coherent structures, such as synchronization domains, in lattice profiles. This approach has potential for many more applications, e.g., in surface roughness analyzes
Y1  - 2006
UR  - http://pre.aps.org/pdf/PRE/v73/i5/e056207
U6  - https://doi.org/10.1103/Physreve.73.056207
ER  - 
TY  - JOUR
A1  - Viana, R. L.
A1  - Grebogi, Celso
A1  - Pinto, S. E. D.
A1  - Lopes, S. R.
A1  - Batista, A. M.
A1  - Kurths, Jürgen
T1  - Bubbling bifurcation : loss of synchronization and shadowing breakdown in complex systems
N2  - Complex dynamical systems with many degrees of freedom may exhibit a wealth of collective phenomena related to high-dimensional chaos. This paper focuses on a lattice of coupled logistic maps to investigate the relationship between the loss of chaos synchronization and the onset of shadowing breakdown 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 manifold. This has been confirmed by numerical diagnostics of synchronization and non-hyperbolic behavior, the latter using the statistical properties of finite-time Lyapunov exponents. (c) 2005 Elsevier B.V. All rights reserved
Y1  - 2005
ER  - 
TY  - JOUR
A1  - De Freitas, M. S. T.
A1  - Viana, R. L.
A1  - Grebogi, Celso
T1  - Basins of attraction of periodic oscillations in suspension bridges
N2  - We consider the dynamics of the lowest order transversal vibration mode of a suspension bridge, for which the hangers are treated as one-sided springs, according to the model of Lazer and McKeena [SIAM Review 58, 1990, 537]. We analyze in particular the multi-stability of periodic attractors and the basin of attraction structure in phase space and its dependence with the model parameters. The parameter values used in numerical simulations have been estimated from a number of bridges built in the United States and in the United Kingdom, thus taking into account realistic, yet sometimes simplified, structural, aerodynamical, and physical considerations
Y1  - 2004
SN  - 0924-090X
ER  - 
TY  - JOUR
A1  - Viana, R. L.
A1  - Grebogi, Celso
A1  - Pinto, Seds
A1  - Lopes, S. R.
A1  - Batista, A. M.
A1  - Kurths, Jürgen
T1  - Validity of numerical trajectories in the synchronization transition of complex systems
N2  - We investigate the relationship between the loss of synchronization and the onset of shadowing breakdown via unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly nonhyperbolic 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 nonhyperbolic properties
Y1  - 2003
SN  - 1063-651X
ER  -