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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)

- 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)

- 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)

- 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)

- F S Borges, P R Protachevicz, +5 authors A M Batista
- Neural networks : the official journal of the…
- 2017

We have studied neuronal synchronisation in a random network of adaptive exponential integrate-and-fire neurons. We study how spiking or bursting synchronous behaviour appears as a function of the coupling strength and the probability of connections, by constructing parameter spaces that identify these synchronous behaviours from measurements of the… (More)

Chemotherapy is a class of cancer treatment that uses drugs to kill cancer cells. A typical chemotherapeu-tic protocol consists of several drugs delivered in cycles of three weeks. We present mathematical analyses demonstrating the existence of a minimum time between cycles of chemotherapy for a protocol to be effective. A mathematical equation is derived,… (More)

- F. S. Borges, P. R. Protachevicz, +5 authors A. M. Batista
- 2016

We have studied neuronal synchronisation in a random network of adaptive exponential integrate-and-fire neurons. We study how spiking or bursting synchronous behaviour appears as a function of the coupling strength and the probability of connections, by constructing parameter spaces that identify these synchronous behaviours from measurements of the… (More)