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- T. Pereira, M. S. Baptista
- 2006

– We present an approach which enables to state about the existence of phase synchronization in coupled chaotic oscillators without having to measure the phase. This is done by observing the oscillators at special times, and analyzing whether this set of points is localized. In particular, we show that this approach is fruitful to analyze the onset of phase… (More)

- C A S Batista, E L Lameu, +5 authors R L Viana
- Physical review. E, Statistical, nonlinear, and…
- 2012

We investigate the collective dynamics of bursting neurons on clustered networks. The clustered network model is composed of subnetworks, each of them presenting the so-called small-world property. This model can also be regarded as a network of networks. In each subnetwork a neuron is connected to other ones with regular as well as random connections, the… (More)

- Yong Zou, Tiago Pereira, Michael Small, Zonghua Liu, Jürgen Kurths
- Physical review letters
- 2014

Spontaneous explosive emergent behavior takes place in heterogeneous networks when the frequencies of the nodes are positively correlated to the node degree. A central feature of such explosive transitions is a hysteretic behavior at the transition to synchronization. We unravel the underlying mechanisms and show that the dynamical origin of the hysteresis… (More)

- Tiago Pereira, Deniz Eroglu, G Baris Bagci, Ugur Tirnakli, Henrik Jeldtoft Jensen
- Physical review letters
- 2013

We study the emergence of coherence in complex networks of mutually coupled nonidentical elements. We uncover the precise dependence of the dynamical coherence on the network connectivity, the isolated dynamics of the elements, and the coupling function. These findings predict that in random graphs the enhancement of coherence is proportional to the mean… (More)

- T. Pereira, J. Kurths
- 2007

We analyze the effect of synchronization in networks of chemically coupled multi-timescale (spiking-bursting) neurons on the process of information transmission within the network. Although, synchronization occurs first in the slow timescale (burst) and then in the fast timescale (spike), we show that information can be transmitted with low probability of… (More)

- T. Pereira, Murilo S. Baptista, Jürgen Kurths, Marcelo B. Reyes
- I. J. Bifurcation and Chaos
- 2007

We study the onset of synchronous states in realistic chaotic neurons coupled by mutually inhibitory chemical synapses. For the realistic parameters, namely the synaptic strength and the intrinsic current, this synapse introduces noncoherences in the neuronal dynamics, yet allowing for chaotic phase synchronization in a large range of parameters. As we… (More)

- T Pereira, M S Baptista, J Kurths
- Physical review. E, Statistical, nonlinear, and…
- 2007

We present an approach which enables one to identify phase synchronization in coupled chaotic oscillators without having to explicitly measure the phase. We show that if one defines a typical event in one oscillator and then observes another one whenever this event occurs, these observations give rise to a localized set. Our result provides a general and… (More)

- Vladimir Vlasov, Yong Zou, Tiago Pereira
- Physical review. E, Statistical, nonlinear, and…
- 2015

Spontaneous explosive is an abrupt transition to collective behavior taking place in heterogeneous networks when the frequencies of the nodes are positively correlated with the node degree. This explosive transition was conjectured to be discontinuous. Indeed, numerical investigations reveal a hysteresis behavior associated with the transition. Here, we… (More)

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… (More)

- T. Pereira, J. Kurths
- 2006

Recently, there has been a great effort to extract the phase of chaotic attractors and complex oscillators. As a consequence many phases have been introduced, as example the standard phase θ based on the rotation of the vector position, and the phase φ based on the rotation of the tangent vector. Despite of the large interest in the phase dynamics of… (More)