Related papers: A Simple Chaotic Neuron Model : Stochastic Behavio…
Traditionally, the neuronal dynamics underlying electroencephalograms (EEG) have been understood as arising from \textit{rhythmic oscillators with varying degrees of synchronization}. This dominant metaphor employs frequency domain EEG…
We consider a continuous-time stochastic model of spiking neurons. In this model, we have a finite or countable number of neurons which are vertices in some graph $G$ where the edges indicate the synaptic connection between them. We focus…
The neural mechanism of memory has a very close relation with the problem of representation in artificial intelligence. In this paper a computational model was proposed to simulate the network of neurons in brain and how they process…
We propose a dynamical neural network model with a hierarchical and modular structure. The network architecture can be derived by minimizing an energy function that is originally designed based on two kinds of neurons with quite different…
We propose a neural network model of multi-neuron interacting system that simulates neurons to interact each other through the surroundings of neuronal cell bodies. We physically model the neuronal cell surroundings, include the dendrites,…
Starting from the concept of binary interactions between pairs of particles, a kinetic framework for the description of the action potential dynamics on a neural network is proposed. It consists of two coupled levels: the description of a…
Chaos provides many interesting properties that can be used to achieve computational tasks. Such properties are sensitivity to initial conditions, space filling, control and synchronization. Chaotic neural models have been devised to…
In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrary fine resolution and arbitrary high…
We study the dynamics of $N$-dimensional lattices of nonchaotic Rulkov neurons coupled with a flow of electrical current. We consider both nearest-neighbor and next-nearest-neighbor couplings, homogeneous and heterogeneous neurons, and…
This paper investigates the origin and onset of chaos in a mathematical model of an individual neuron, arising from the intricate interaction between 3D fast and 2D slow dynamics governing its intrinsic currents. Central to the chaotic…
Large networks of sparsely coupled, excitatory and inhibitory cells occur throughout the brain. A striking feature of these networks is that they are chaotic. How does this chaos manifest in the neural code? Specifically, how variable are…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
General results from statistical learning theory suggest to understand not only brain computations, but also brain plasticity as probabilistic inference. But a model for that has been missing. We propose that inherently stochastic features…
Recurrent neural networks (RNNs) with random, but sufficiently strong and balanced coupling display a well known high-dimensional chaotic dynamics. Here, we investigate if externally applied inputs to these RNNs can stabilize globally…
In 2018, Ferrari et al. wrote a paper called "Phase Transition for Infinite Systems of Spiking Neurons" in which they introduced a continuous time stochastic model of interacting neurons. This model has a parameter $\gamma$, corresponding…
The dynamics of neural networks is often characterized by collective behavior and quasi-synchronous events, where a large fraction of neurons fire in short time intervals, separated by uncorrelated firing activity. These global temporal…
We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…
We consider the theoretical constraints on interactions between coupled cortical columns. Each column comprises a set of neural populations, where each population is modelled as a neural mass. The existence of semi-stable states within a…
The dynamics of an extremely diluted neural network with high order synapses acting as corrections to the Hopfield model is investigated. As in the fully connected case, the high order terms may strongly improve the storage capacity of the…
We study two population models describing the dynamics of interacting neurons, initially proposed by Pakdaman, Perthame, and Salort (2010, 2014). In the first model, the structuring variable $s$ represents the time elapsed since its last…