TY  - JOUR
A1  - Pereira, Tiago
A1  - Baptista, Murilo da Silva
A1  - Reyes, Marcelo B.
A1  - Caldas, Ibere Luiz
A1  - Sartorelli, José Carlos
A1  - Kurths, Jürgen
T1  - A scenario for torus T-2 destruction via a global bifurcation
N2  - We show a scenario of a two-frequeney torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T-2 with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle points. Moreover, we present detailed evidences of a heteroclinic saddle-focus orbit responsible for the type- if intermittency induced by this global bifurcation. We also characterize this transition to chaos by measuring the Lyapunov exponents and the scaling laws.
Y1  - 2009
UR  - http://www.sciencedirect.com/science/journal/09600779
U6  - https://doi.org/10.1016/j.chaos.2007.06.115
SN  - 0960-0779
ER  - 
TY  - JOUR
A1  - Pereira, Tiago
A1  - Baptista, Murilo da Silva
A1  - Reyes, Marcelo Bussotti
A1  - Caldas, Ibere Luiz
A1  - Sartorelli, José Carlos
A1  - Kurths, Jürgen
T1  - Global bifurcation destroying the experimental torus T-2
N2  - We show experimentally the scenario of a two-frequency torus T-2 breakdown, in which a global bifurcation occurs due to the collision of a torus with an unstable periodic orbit, creating a heteroclinic saddle connection, followed by an intermittent behavior
Y1  - 2006
UR  - http://pre.aps.org/
U6  - https://doi.org/10.1103/Physreve.73.017201
ER  - 
TY  - JOUR
A1  - Baptista, Murilo da Silva
A1  - Pereira, Tiago
A1  - Sartorelli, J. C.
A1  - Caldas, Ibere Luiz
A1  - Kurths, Jürgen
T1  - Non-transitive maps in phase synchronization
N2  - Concepts from Ergodic Theory are used to describe the existence of special non-transitive maps in attractors of phase synchronous chaotic oscillators. In particular, it is shown that, for a class of phase-coherent oscillators, these special maps imply phase synchronization. We illustrate these ideas in the sinusoidally forced Chua's circuit and two coupled Rossler oscillators. Furthermore, these results are extended to other coupled chaotic systems. In addition, a phase for a chaotic attractor is defined from the tangent vector of the flow. Finally, it is discussed how these maps can be used for the real-time detection of phase synchronization in experimental systems. (c) 2005 Elsevier B.V. All rights reserved
Y1  - 2005
ER  - 
TY  - JOUR
A1  - Baptista, Murilo da Silva
A1  - Pereira, Tiago
A1  - Kurths, Jürgen
T1  - Upper bounds in phase synchronous weak coherent chaotic attractors
N2  - An approach is presented for coupled chaotic systems with weak coherent motion, from which we estimate the upper bound value for the absolute phase difference in phase synchronous states. This approach shows that synchronicity in phase implies synchronicity in the time of events, a characteristic explored to derive an equation to detect phase synchronization, based on the absolute difference between the time of these events. We demonstrate the potential use of this approach for the phase coherent and the funnel attractor of the Rossler system, as well as for the spiking/bursting Rulkov map.
Y1  - 2006
UR  - http://www.sciencedirect.com/science/journal/01672789
U6  - https://doi.org/10.1016/j.physd.2006.02.007
SN  - 0167-2789
ER  -