Cecilia Romaro, Fernando Araujo Najman, Morgan André
In this paper we present a numerical study of a mathematical model of spiking neurons introduced by Ferrari et al. in an article entitled Phase transition forinfinite systems of spiking neurons. In this model we have a countable number of neurons linked together in a network, each of them having a membrane potential taking value in the integers, and each of them spiking over time at a rate which depends on the membrane potential through some rate function ϕ. Beside being affected by a spike each neuron can also be affected by leaking. At each of these leak times, which occurs for a given neuron at a fixed rate γ, the membrane potential of the neuron concerned is spontaneously reset to 0.
The Research, Innovation and Dissemination Center on Neuromathematics (RIDC NeuroMat) is offering scholarships for information technology professionals interested in being part of a breakthrough and innovative scientific project.
The Research, Innovation and Dissemination Center on Neuromathematics (RIDC NeuroMat) is offering a scholarship for data and computational statistics scientists or professionals from related areas interested in being part of a breakthrough and innovative scientific project.
The Research, Innovation and Dissemination Center on Neuromathematics (RIDC NeuroMat) is offering a scholarship for information technology professionals interested in being part of a breakthrough and innovative scientific project.
Antonio Galves, Eva Löcherbach, Christophe Pouzat, Errico Presutti
In this paper we present a simple microscopic stochastic model describing short term plasticity within a large homogeneous network of interacting neurons. Each neuron is represented by its membrane potential and by the residual calcium concentration within the cell at a given time. Neurons spike at a rate depending on their membrane potential. When spiking, the residual calcium concentration of the spiking neuron increases by one unit. Moreover, an additional amount of potential is given to all other neurons in the system. This amount depends linearly on the current residual calcium concentration within the cell of the spiking neuron. In between successive spikes, the potentials and the residual calcium concentrations of each neuron decrease at a constant rate.
