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- C. A. S. Batista, S. R. Lopes, Ricardo L. Viana, Antonio M. Batista
- Neural Networks
- 2010

Several neurological diseases (e.g. essential tremor and Parkinson's disease) are related to pathologically enhanced synchronization of bursting neurons. Suppression of these synchronized rhythms has potential implications in electrical deep-brain stimulation research. We consider a simplified model of a neuronal network where the local dynamics presents a… (More)

- C A S Batista, A M Batista, J A C de Pontes, R L Viana, S R Lopes
- Physical review. E, Statistical, nonlinear, and…
- 2007

There is experimental evidence that the neuronal network in some areas of the brain cortex presents the scale-free property, i.e., the neuron connectivity is distributed according to a power law, such that neurons are more likely to couple with other already well-connected ones. From the information processing point of view, it is relevant that neuron… (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)

- E L Lameu, C A S Batista, +4 authors J Kurths
- Chaos
- 2012

Functional brain networks are composed of cortical areas that are anatomically and functionally connected. One of the cortical networks for which more information is available in the literature is the cat cerebral cortex. Statistical analyses of the latter suggest that its structure can be described as a clustered network, in which each cluster is a… (More)

- Kelly C Iarosz, Fernando S Borges, +4 authors Sergio R Lopes
- Journal of theoretical biology
- 2015

In recent years, it became clear that a better understanding of the interactions among the main elements involved in the cancer network is necessary for the treatment of cancer and the suppression of cancer growth. In this work we propose a system of coupled differential equations that model brain tumour under treatment by chemotherapy, which considers… (More)

- D B Vasconcelos, S R Lopes, R L Viana, J Kurths
- Physical review. E, Statistical, nonlinear, and…
- 2006

We propose an extension of the recurrence plot concept to perform quantitative analyzes of roughness and disorder of spatial patterns at a fixed time. We introduce spatial recurrence plots (SRPs) as a graphical representation of the pointwise correlation matrix, in terms of a two-dimensional spatial return plot. This technique is applied to the study of… (More)

- F. S. Borges, K. C. Iarosz, +5 authors Celso Grebogi
- Biosystems
- 2014

In this work we investigate a mathematical model describing tumour growth under a treatment by chemotherapy that incorporates time-delay related to the conversion from resting to hunting cells. We study the model using values for the parameters according to experimental results and vary some parameters relevant to the treatment of cancer. We find that our… (More)

- T de L Prado, S R Lopes, C A S Batista, J Kurths, R L Viana
- Physical review. E, Statistical, nonlinear, and…
- 2014

We considered a clustered network of bursting neurons described by the Huber-Braun model. In the upper level of the network we used the connectivity matrix of the cat cerebral cortex network, and in the lower level each cortex area (or cluster) is modelled as a small-world network. There are two different coupling strengths related to inter- and… (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)

- S R Lopes, F B Rizzato
- Physical review. E, Statistical physics, plasmas…
- 1999

In this paper we examine the coupling of two wave triplets sharing two common modes. The analysis is performed in the solitonic sector of the parameter space where uncoupled solutions departing from linearly unstable homogeneous initial conditions evolve into a collection of regularly interspersed, spatiotemporally localized spikes. The uncoupled system is… (More)