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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)

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)

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, A M Batista, K Iarosz, R L Viana, S R Lopes +1 other
- 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)

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)

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)

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)

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)

Bursting neurons fire rapid sequences of action potential spikes followed by a quiescent period. The basic dynamical mechanism of bursting is the slow currents that modulate a fast spiking activity caused by rapid ionic currents. Minimal models of bursting neurons must include both effects. We considered one of these models and its relation with a… (More)

We investigated the transition to wave turbulence in a spatially extended three-wave interacting model, where a spatially homogeneous state undergoing chaotic dynamics undergoes spatial mode excitation. The transition to this weakly turbulent state can be regarded as the loss of synchronization of chaos of mode oscillators describing the spatial dynamics.