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)
The cortical processing of visual information begins at the primary visual area of the cerebral cortex (V1). It maps completely the visual field, receiving input from the Lateral Gineculate Nucleus (LGN) and transmitting the output to the secondary visual area (V2). Recently, Andreazza and Pinto have proposed a biologically motivated network of neurons in(More)
Neural synchronization is a phenomenon related to information transmission between brain areas, cognitive functions, perceptual and motor skills and memory [1,2], and also connected to mental illnesses like epilepsy , isolated seizures, Alzheimer´s disease, Parkinson´s disease, autism and schizophrenia [3]. This work is related to the critical state of the(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)
The KTz neuron model [1-5] is a map with three dynamic variables: the neuron membrane potential (xt), a recovery variable (y t) and a slow adaptive current (zt), given by the following equations: x t+1 = tanh x t − Ky t + z t + I t T , y t+1 = x t , z t+1 = (1 − δ) z t − λ (x t − x R) , where δ is related to the refractory period, x R is the reversal(More)