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- 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, 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)

- 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)

- 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)

- C A S Batista, R L Viana, F A S Ferrari, S R Lopes, A M Batista, J C P Coninck
- Physical review. E, Statistical, nonlinear, and…
- 2013

Thermally sensitive neurons present bursting activity for certain temperature ranges, characterized by fast repetitive spiking of action potential followed by a short quiescent period. Synchronization of bursting activity is possible in networks of coupled neurons, and it is sometimes an undesirable feature. Control procedures can suppress totally or… (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)

- Ewandson L Lameu, Fernando S Borges, +5 authors Jürgen Kurths
- Chaos
- 2016

We have studied the effects of perturbations on the cat's cerebral cortex. According to the literature, this cortex structure can be described by a clustered network. This way, we construct a clustered network with the same number of areas as in the cat matrix, where each area is described as a sub-network with a small-world property. We focus on the… (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)