Pereira, Rodrigo Frehse, Viana, Ricardo L., Lopes, Sergio R., Grebogi, Celso
Many chaotic dynamical systems of physical interest present a strong form of nonhyperbolicity called unstable dimension variability (UDV), for which the chaotic invariant set contains periodic orbits...
Random fluctuation leads to forbidden escape of particles (2009)
Rodrigues, Christian S., Grebogi, Celso
A great number of physical processes are described within the context of Hamiltonian scattering. Previous studies have rather focused on trajectories starting outside invariant structures, since the...
Emerging attractors and the transition from dissipative to conservative dynamics (2008)
Rodrigues, Christian S., Grebogi, Celso
The topological structure of basin boundaries plays a fundamental role in the sensitivity to the initial conditions in chaotic dynamical systems. Herewith we present a study on the dynamics of...
Signatures of fractal clustering of aerosols advected under gravity (2007)
Vilela, Rafael Dias, Tél, Tamás, Grebogi, Celso
Aerosols under chaotic advection often approach a strange attractor. They move chaotically on this fractal set but, in the presence of gravity, they have a net vertical motion downwards. In practical...
The multifractal fly: a dynamically multilayered visual system (2007)
Baptista, M. S., Grebogi, Celso, Köberle, Roland
We dynamically analyze our experimental results on the motion sensitive spiking H1 neuron of the fly's visual system. We find that the fly uses an alphabet composed of a few letters to encode the...
Simulating a Chaotic Process (2006)
Ricardo L. Viana, Celso Grebogi, Antônio M. Batista
Simulating a Chaotic Process
Finite-size effects on open chaotic advection (2005)
Vilela, Rafael Dias, Grebogi, Celso
We study the effects of finite-sizeness on small, neutrally buoyant, spherical particles advected by open chaotic flows. We show that, when projected onto configuration space, the advected...
Effective dynamics in Hamiltonian systems with mixed phase space (2005)
Motter, Adilson E., Grebogi, Celso, Kantz, Holger
An adequate characterization of the dynamics of Hamiltonian systems at physically relevant scales has been largely lacking. Here we investigate this fundamental problem and we show that the...
Simulating a chaotic process (2005)
Viana,Ricardo L., Barbosa,José R. R., Grebogi,Celso, Batista,Antônio M.
Computer simulations of partial differential equations of mathematical physics typically lead to some kind of high-dimensional dynamical system. When there is chaotic behavior we are faced with...
Poincare recurrence and measure of hyperbolic and nonhyperbolic chaotic attractors (2004)
Baptista, Murilo S., Kraut, Suso, Grebogi, Celso
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 not supported...
Stability Properties of Nonhyperbolic Chaotic Attractors under Noise (2004)
We study local and global stability of nonhyperbolic chaotic attractors contaminated by noise. The former is given by the maximum distance of a noisy trajectory from the noisefree attractor, while...
Universality in active chaos (2004)
Tel, Tamas, Nishikawa, Takashi, Motter, Adilson E., Grebogi, Celso, Toroczkai, Zoltan
Many examples of chemical and biological processes take place in large-scale environmental flows. Such flows generate filamental patterns which are often fractal due to the presence of chaos in the...
Reactive dynamics of inertial particles in nonhyperbolic chaotic flows (2003)
Motter, Adilson E., Lai, Ying-Cheng, Grebogi, Celso
Anomalous kinetics of infective (e.g., autocatalytic) reactions in open, nonhyperbolic chaotic flows are important for many applications in biological, chemical, and environmental sciences. We...
Escaping from nonhyperbolic chaotic attractors (2003)
We study the noise-induced escape process from chaotic attractors in nonhyperbolic systems. We provide a general mechanism of escape in the low noise limit, employing the theory of large...
TOPOLOGY OF WINDOWS IN THE HIGH-DIMENSIONAL PARAMETER SPACE OF CHAOTIC MAPS (2003)
Murilo S. Baptista, Celso Grebogi, Ernest Barreto
Periodicity is ubiquitous in nature. In this work, we analyze the dynamical reasons for which periodic windows, that appear in parameter space diagrams, have different shapes and structures. For...
Output functions and fractal dimensions in dynamical systems (2001)
We present a novel method for the calculation of the fractal dimension of boundaries in dynamical systems, which is in many cases many orders of magnitude more efficient than the uncertainty method....
Soumitro Banerjee, Priya Ranjan, Celso Grebogi
Recent investigations on the bifurcation behavior of power electronic dc-dc converters has revealed that most of the observed bifurcations do not belong to generic classes like saddle-node, period...
Unstable dimension variability and synchronization of chaotic systems (1999)
Viana, Ricardo L., Grebogi, Celso
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...
International Journal of Bifurcation and Chaos, Vol. 10, No. 3 (2000) 683 693 (1999)
World Scientific Publishing, Ying-cheng Lai, Celso Grebogi
this paper, that there exists a class of models of chaotic processes, for which severe obstruction to deterministic modeling may arise. In particular, such obstruction may occur when unstable...
Blowout bifurcation of chaotic saddles (1999)
Tomasz Kapitaniak, Ying-Cheng Lai, Celso Grebogi
Chaotic saddles are nonattracting dynamical invariant sets that can lead to a variety of physical phenomena. We describe the blowout bifurcation of chaotic saddles located in the symmetric invariant...
Numerical Procedures for Analyzing Dynamical Processes. (1998)
Grebogi, Celso, Ott, Edward, Yorke, James A.
We are delivering a tape with a software package for UNIX workstations with documentation for analyzing low dimensional dynamical behavior from time series. In particular, the Lyapunov exponent code...
Information Transmission Using Chaos. (1998)
Hayes, Scott, Grebogi, Celso, Ott, Edward
The use of chaos to transmit information is described. Chaotic dynamical systems, such as electrical oscillators with very simple structures, naturally produce complex waveforms. We show that the...
Guiding Center Hamiltonian Theory of Free-Electron Lasers (1998)
The relativistic guiding center ponderomotive Hamiltonian for free electron lasers is derived. The derivation takes into account arbitrary signal wave polarization and wiggler field geometry...
Active Chaotic Flows, Deterministic Modeling, and Communication with Chaos (1998)
This is the final report on this project. The objectives were threefold: (1) to study the chemical and biological activity in environmental flows often involving larger particles which are influenced...
Border Collision Bifurcations in Two Dimensional Piecewise Smooth Maps (1998)
Banerjee, Soumitro, Grebogi, Celso
Recent investigations on the bifurcations in switching circuits have shown that many atypical bifurcations can occur in piecewise smooth maps which can not be classified among the generic cases like...
Banerjee, Soumitro, Yorke, James A., Grebogi, Celso
It has been proposed to make practical use of chaos in communication, in enhancing mixing in chemical processes and in spreading the spectrum of switch-mode power suppies to avoid electromagnetic...
Blowout bifurcation of chaotic saddles (1998)
Tomasz Kapitaniak, Ying-Cheng Lai, Celso Grebogi
Chaotic saddles are nonattracting dynamical invariant sets that can lead to a variety of physical phenomena. We describe the blowout bifurcation of chaotic saddles located in the symmetric invariant...
How good and for how long: Scaling laws on validity of trajectories (1997)
Tim Sauer, Celso Grebogi, James A. Yorke
Dynamical conditions for the loss of validity of numerical chaotic solutions of physical systems are already understood. However, the fundamental questions of "how good" and "for how...