Marcelo H. R. Tragtenberg

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We study a simple map as a minimal model of excitable cells. The map has two fast variables which mimic the behavior of class I neurons, undergoing a sub-critical Hopf bifurcation. Adding a third slow variable allows the system to present bursts and other interesting biological behaviors. Bifurcation lines which locate the excitability region are obtained(More)
Many different kinds of noise are experimentally observed in the brain. Among them, we study a model of noisy chemical synapse and obtain critical avalanches for the spatiotemporal activity of the neural network. Neurons and synapses are modeled by dynamical maps. We discuss the relevant neuronal and synaptic properties to achieve the critical state. We(More)
This review gives a short historical account of the excitable maps approach for modeling neurons and neuronal networks. Some early models, due to Pasemann (1993), Chialvo (1995) and Kinouchi and Tragtenberg (1996), are compared with more recent proposals by Rulkov (2002) and Izhikevich (2003). We also review map-based schemes for electrical and chemical(More)
We study a new biologically motivated model for the Macaque monkey primary visual cortex which presents power-law avalanches after a visual stimulus. The signal propagates through all the layers of the model via avalanches that depend on network structure and synaptic parameter. We identify four different avalanche profiles as a function of the excitatory(More)
To study neurons with computational tools, one may call upon, at least, two different approaches: (i) Hodgkin-Huxley like neurons [1] (i.e. biological neurons) and (ii) formal neurons (e.g. Hindmarsh-Rose (HR) model [2], Kinouchi-Tragtenberg (KT) model [3], etc). Formal neurons may be represented by ordinary differential equations (e.g. HR), or by maps,(More)
We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following one of two deterministic aperiodic sequences, the Fibonacci or period-doubling one. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the(More)
where δ is related to the refractory period, xR is the reversal potential, λ controls the burst sizes, It is an external current and K and T are gain parameters for neuron self-interactions. The hyperbolic tangent is biologically plausible, since it is a sigmoidal function that saturates at large absolute inputs. This model exhibits a rich repertoire of(More)
We introduce a new map-based neuron model derived from the dynamical perceptron family that has the best compromise between computational efficiency, analytical tractability, reduced parameter space and many dynamical behaviors. We calculate bifurcation and phase diagrams analytically and computationally that underpins a rich repertoire of autonomous and(More)