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- Ricardo L. Viana, S. E. de S. Pinto, J. R. R. Barbosa, Celso Grebogi
- I. J. Bifurcation and Chaos
- 2003

We call a chaotic dynamical system pseudo-deterministic when it does not produce numerical, or pseudo-trajectories that stay close, or shadow chaotic true trajectories, even though the model equations are strictly deterministic. In this case, single chaotic trajectories may not be meaningful, and only statistical predictions, at best, could be drawn on the… (More)

- Ricardo L Viana, Sandro E de S Pinto, Celso Grebogi
- Physical review. E, Statistical, nonlinear, and…
- 2002

Dynamical systems possessing symmetries have invariant manifolds. According to the transversal stability properties of this invariant manifold, nearby trajectories may spend long stretches of time in its vicinity before being repelled from it as a chaotic burst, after which the trajectories return to their original laminar behavior. The onset of chaotic… (More)

- Antônio M Batista, Sandro E de S Pinto, Ricardo L Viana, Sergio R Lopes
- Physical review. E, Statistical, nonlinear, and…
- 2002

We study the synchronization properties of a lattice of chaotic piecewise linear maps. The coupling strength decreases with the lattice distance in a power-law fashion. We obtain the Lyapunov spectrum of the coupled map lattice and investigate the relation between spatiotemporal chaos and synchronization of amplitudes and phases, using suitable numerical… (More)

- Celia Anteneodo, Sandro E de S Pinto, Antônio M Batista, Ricardo L Viana
- Physical review. E, Statistical, nonlinear, and…
- 2003

We obtain exact analytical results for lattices of maps with couplings that decay with distance as r(-alpha). We analyze the effect of the coupling range on the system dynamics through the Lyapunov spectrum. For lattices whose elements are piecewise linear maps, we get an algebraic expression for the Lyapunov spectrum. When the local dynamics is given by a… (More)

Frequency synchronization is a common phenomenon in spatially extended dynamical systems, like oscillator chains and coupled map lattices. We study the distribution of synchronization plateaus in a sine-circle map lattice with a variable range coupling and randomly distributed natural frequencies. A transition between synchronized and nonsynchronized phases… (More)

- S E de S Pinto, I L Caldas, A M Batista, S R Lopes, R L Viana
- Physical review. E, Statistical, nonlinear, and…
- 2007

A lattice of coupled chaotic dynamical systems may exhibit a completely synchronized state, which defines a low-dimensional invariant manifold in phase space. However, the high dimensionality of the latter typically yields a complex dynamics with many features like chaos suppression, quasiperiodicity, multistability, and intermittency. Such phenomena are… (More)

- R F Pereira, R L Viana, S R Lopes, M C Vergès, S E de S Pinto
- Physical review. E, Statistical, nonlinear, and…
- 2011

In the presence of unstable dimension variability numerical solutions of chaotic systems are valid only for short periods of observation. For this reason, analytical results for systems that exhibit this phenomenon are needed. Aiming to go one step further in obtaining such results, we study the parametric evolution of unstable dimension variability in two… (More)

- R L Viana, C Grebogi, S E de S Pinto, S R Lopes, A M Batista, J Kurths
- Physical review. E, Statistical, nonlinear, and…
- 2003

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… (More)

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