Related papers: Analysis of a map-based neuronal model
At functional scales, cortical behavior results from the complex interplay of a large number of excitable cells operating in noisy environments. Such systems resist to mathematical analysis, and computational neurosciences have largely…
Background/Introduction: In this paper, the neural network class of Self-Organising Maps (SOMs) is investigated in terms of its theoretical and applied validity for cognitive modelling, particularly of neurodevelopmental disorders. Methods:…
Most models of neurons incorporate a capacitor to account for the marked capacitive behavior exhibited by the cell membrane. However, such capacitance is widely considered constant, thereby neglecting the possible effects of time-dependent…
We propose a stochastic dynamical model of noisy neural networks with complex architectures and discuss activation of neural networks by a stimulus, pacemakers and spontaneous activity. This model has a complex phase diagram with…
Neurons are subject to various kinds of noise. In addition to synaptic noise, the stochastic opening and closing of ion channels represents an intrinsic source of noise that affects the signal processing properties of the neuron. In this…
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…
We study the stable phases of an attractor neural network model, with binary units, for hippocampal place cells encoding 1D or 2D spatial maps or environments. Using statistical mechanics tools we show that, below critical values for the…
A mathematical model is developed, to jointly analyze elastic and inelastic scattering data of fluctuating membranes within a single theoretical framework. The model builds on a non-homogeneously clipped time-dependent Gaussian random…
We study an abstracted model of neuronal activity via numerical simulation, and report spatiotemporal pattern formation and critical like dynamics. A population of pulse coupled, discretised, relaxation oscillators is simulated over…
We investigate the modes of oscillation of heterogeneous ring-networks of quadratic integrate-and-fire neurons with non-local, space-dependent coupling. Perturbations of the equilibrium state with a particular wave number produce transient…
We study the asymptotic behavior for asymmetric neuronal dynamics in a network of linear Hopfield neurons. The interaction between the neurons is modeled by random couplings which are centered i.i.d. random variables with finite moments of…
A simple model that replicates the dynamics of spiking and spiking-bursting activity of real biological neurons is proposed. The model is a two-dimensional map which contains one fast and one slow variable. The mechanisms behind generation…
A piecewise continuous map for modeling bursting and spiking behaviour of isolated neuron is proposed. The map was created from phenomenological viewpoint. The map demonstrates oscillations, which are qualitatively similar to oscillations…
Here we numerically study a model of excitable media, namely, a network with occasionally quiet nodes and connection weights that vary with activity on a short-time scale. Even in the absence of stimuli, this exhibits unstable dynamics,…
In this paper we address the question of statistical model selection for a class of stochastic models of biological neural nets. Models in this class are systems of interacting chains with memory of variable length. Each chain describes the…
Neurons in the nervous system are submitted to distinct sources of noise, such as ionic-channel and synaptic noise, which introduces variability in their responses to repeated presentations of identical stimuli. This motivates the use of…
A networked oscillator based analysis is performed for periodic bluff body flows to examine and control the transfer of kinetic energy. Spatial modes extracted from the flow field with corresponding amplitudes form a set of oscillators…
Can we use spiking neural networks (SNN) as generative models of multi-neuronal recordings, while taking into account that most neurons are unobserved? Modeling the unobserved neurons with large pools of hidden spiking neurons leads to…
Brain rhythms contribute to every aspect of brain function. Here, we study critical and resonance phenomena that precede the emergence of brain rhythms. Using an analytical approach and simulations of a cortical circuit model of neural…
We consider a system of $N$ neurons, each spiking randomly with rate depending on its membrane potential. When a neuron spikes, its potential is reset to $0$ and all other neurons receive an additional amount $h/N$ of potential, where $ h >…