TY - JOUR
A1 - Baptista, Murilo S.
A1 - Kraut, Suso
A1 - Grebogi, Celso
T1 - Poincare recurrence and measure of hyperbolic and nonhyperbolic chaotic attractors
N2 - We study Poincare recurrence of chaotic attractors for regions of finite size. Contrary to the standard case, where the size of the recurrent regions tends to zero, the measure is no longer supported solely by unstable periodic orbits of finite length inside it, but also by other special recurrent trajectories, located outside that region. The presence of the latter leads to a deviation of the distribution of the Poincare first return times from a Poissonian. Consequently, by taking into account the contribution of these special recurrent trajectories, a corrected estimate of the measure is obtained. This has wide experimental implications, as in the laboratory all returns can exclusively be observed for regions of finite size, and only unstable periodic orbits of finite length can be detected
Y1 - 2005
SN - 0031-9007
ER -
TY - JOUR
A1 - Viana, Ricardo L.
A1 - Barbosa, José R. R.
A1 - Grebogi, Celso
T1 - Unstable dimension variability and codimension-one bifurcations of two-dimensional maps
N2 - Unstable dimension variability is a mechanism whereby an invariant set of a dynamical system, like a chaotic attractor or a strange saddle, loses hyperbolicity in a severe way, with serious consequences on the shadowability properties of numerically generated trajectories. In dynamical systems possessing a variable parameter, this phenomenon can be triggered by the bifurcation of an unstable periodic orbit. This Letter aims at discussing the possible types of codimension-one bifurcations leading to unstable dimension variability in a two-dimensional map, presenting illustrative examples and displaying numerical evidences of this fact by computing finite-time Lyapunov exponents. (C) 2004 Elsevier B.V. All rights reserved
Y1 - 2004
SN - 0375-9601
ER -
TY - JOUR
A1 - Kraut, Suso
A1 - Feudel, Ulrike
A1 - Grebogi, Celso
T1 - Preference of attractors in noisy multistable systems
Y1 - 1999
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 - Karolyi, G.
A1 - Tel, Tomas
A1 - de Moura, A. P. S.
A1 - Grebogi, Celso
T1 - Reactive particles in random flows
N2 - We study the dynamics of chemically or biologically active particles advected by open flows of chaotic time dependence, which can be modeled by a random time dependence of the parameters on a stroboscopic map. We develop a general theory for reactions in such random flows, and derive the reaction equation for this case. We show that there is a singular enhancement of the reaction in random flows, and this enhancement is increased as compared to the nonrandom case. We verify our theory in a model flow generated by four point vortices moving chaotically
Y1 - 2004
SN - 0031-9007
ER -
TY - JOUR
A1 - Karolyi, György
A1 - Pentek, Aron
A1 - Toroczkai, Zoltán
A1 - Tél, Tómas
A1 - Grebogi, Celso
T1 - Advection of active particles in open chaotic flows
Y1 - 1998
SN - 0031-9007
ER -
TY - JOUR
A1 - Poon, L.
A1 - Grebogi, Celso
A1 - Feudel, Ulrike
A1 - Yorke, J. A.
T1 - Dynamical properties of a simple mechanical system with a large number of coexisting periodic attractors
Y1 - 1998
ER -
TY - JOUR
A1 - Lai, Ying Cheng
A1 - Grebogi, Celso
A1 - Feudel, Ulrike
A1 - Witt, Annette
T1 - Basin bifurcation in quasiperiodically forced systems
Y1 - 1998
ER -
TY - JOUR
A1 - Hunt, Brain R.
A1 - Grebogi, Celso
A1 - Barreto, Ernest
A1 - Yorke, James A.
T1 - From high dimensional chaos to stable periodic orbits : the structure of parameter space
Y1 - 1997
ER -
TY - JOUR
A1 - Rosa, Epaminondas
A1 - Hayes, S.
A1 - Grebogi, Celso
T1 - Noise filtering in communication with chaos
Y1 - 1997
ER -
TY - JOUR
A1 - Sauer, T.
A1 - Grebogi, Celso
A1 - Yorke, J. A.
T1 - How long do numerical chaotic solutions remain valid?
Y1 - 1997
ER -
TY - JOUR
A1 - Bolt, Eric
A1 - Lai, Ying Cheng
A1 - Grebogi, Celso
T1 - Coding, channel capacity and noise resistance in communication with chaos
Y1 - 1997
ER -
TY - JOUR
A1 - Feudel, Ulrike
A1 - Grebogi, Celso
T1 - Multistability and the control of complexity
Y1 - 1997
SN - 1054-1500
ER -
TY - JOUR
A1 - Feudel, Ulrike
A1 - Grebogi, Celso
A1 - Ott, E.
T1 - Phase-locking in quasiperiodically forced systems
Y1 - 1997
ER -
TY - JOUR
A1 - Grebogi, Celso
A1 - Lai, Ying Cheng
T1 - Controlling chaos in high dimensions
Y1 - 1997
ER -
TY - JOUR
A1 - Grebogi, Celso
A1 - Lai, Ying Cheng
T1 - Controlling chaotic dynamical systems
Y1 - 1997
ER -
TY - JOUR
A1 - Grebogi, Celso
A1 - Lai, Ying Cheng
A1 - Hayes, S.
T1 - Control and applications of chaos
Y1 - 1997
SN - 0016-0032
ER -
TY - JOUR
A1 - Lai, Ying Cheng
A1 - Nagai, Y.
A1 - Grebogi, Celso
T1 - Characterization of the natural measure by unstable periodic orbits in chaotic attractors
Y1 - 1997
ER -
TY - JOUR
A1 - Feudel, Fred
A1 - Witt, Annette
A1 - Gellert, Marcus
A1 - Kurths, Jürgen
A1 - Grebogi, Celso
A1 - Sanjuan, Miguel Angel Fernandez
T1 - Intersections of stable and unstable manifolds : the skeleton of Lagrangian chaos
N2 - We study Hamiltonian chaos generated by the dynamics of passive tracers moving in a two-dimensional fluid flow and describe the complex structure formed in a chaotic layer that separates a vortex region from the shear flow. The stable and unstable manifolds of unstable periodic orbits are computed. It is shown that their intersections in the Poincare map as an invariant set of homoclinic points constitute the backbone of the chaotic layer. Special attention is paid to the finite time properties of the chaotic layer. In particular, finite time Lyapunov exponents are computed and a scaling law of the variance of their distribution is derived. Additionally, the box counting dimension as an effective dimension to characterize the fractal properties of the layer is estimated for different duration times of simulation. Its behavior in the asymptotic time limit is discussed. By computing the Lyapunov exponents and by applying methods of symbolic dynamics, the formation of the layer as a function of the external forcing strength, which in turn represents the perturbation of the originally integrable system, is characterized. In particular, it is shown that the capture of KAM tori by the layer has a remarkable influence on the averaged Lyapunov exponents. (C) 2004 Elsevier Ltd. All rights reserved
Y1 - 2005
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 - 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 -
TY - JOUR
A1 - Lai, Ying Cheng
A1 - Grebogi, Celso
A1 - Kurths, Jürgen
T1 - Modeling of deterministic chaotic systems
Y1 - 1999
ER -
TY - JOUR
A1 - Schwarz, Udo
A1 - Spahn, Frank
A1 - Grebogi, Celso
A1 - Kurths, Jürgen
A1 - Petzschmann, Olaf
T1 - Length scales of clustering in granular gases
Y1 - 1999
ER -