Related papers: Asymptotic behaviour of neuron population models s…
Randomly connected neural networks have long served as a theoretical tool for studying collective dynamics in neural populations, yet quantitative comparisons to experiments remain limited. Recent technological advances have made it…
We study the expressive power of positive neural networks. The model uses positive connection weights and multiple input neurons. Different behaviors can be expressed by varying the connection weights. We show that in discrete time, and in…
We investigate dynamical systems characterized by a time series of distinct semi-stable activity patterns, as they are observed in cortical neural activity patterns. We propose and discuss a general mechanism allowing for an adiabatic…
The static synaptic connectivity of neuronal circuits stands in direct contrast to the dynamics of their function. As in changing community interactions, different neurons can participate actively in various combinations to effect behaviors…
Neural population activity exhibits complex, nonlinear dynamics, varying in time, over trials, and across experimental conditions. Here, we develop Conditionally Linear Dynamical System (CLDS) models as a general-purpose method to…
Several experiments and models have highlighted the importance of neuronal heterogeneity in brain dynamics and function. However, how such a cell-to-cell diversity can affect cortical computation, synchronization, and neuronal communication…
In this paper we study collective decision making on a multi-population, represented by a regular network of groups of individuals. Each group consists of a collection of players and every player can choose between two options. A group is…
We have shortly reviewed the occurrence of the post-synaptic potentials between neurons, the relation between EEG and neuron dynamics, as well as methods of signal analysis. We supposed a simple stochastic model representing electrical…
In this paper, we consider a model of impulsive recurrent neural networks with piecewise constant delay. The dynamics are presented by differential equations with discontinuities such as impulses at fixed moments and piecewise constant…
We consider an extension of the Rescorla-Wagner model which bridges the gap between conditioning and learning on a neural-cognitive, individual psychological level, and the social population level. In this model, the interaction among…
We derive asymptotic properties for a stochastic dynamic network model in a stochastic dynamic population. In the model, nodes give birth to new nodes until they die, each node being equipped with a social index given at birth. During the…
One of the main challenges in the study of time-varying networks is the interplay of memory effects with structural heterogeneity. In particular, different nodes and dyads can have very different statistical properties in terms of both link…
Excitatory and inhibitory nonlinear noisy leaky integrate and fire models are often used to describe neural networks. Recently, new mathematical results have provided a better understanding of them. It has been proved that a fully…
Complexity in the temporal organization of neural systems may be a reflection of the diversity of its neural constituents. These constituents, excitatory and inhibitory neurons, comprise an invariant ratio in vivo and form the substrate for…
A novel approach to moment closure problem is used to derive low dimensional laws for the dynamics of the moments of the membrane potential distribution in a population of spiking neurons. Using spectral expansion of the density equation we…
Advances in simultaneous recordings of large numbers of neurons have driven significant interest in the structure of neural population activity such as dimension. A key question is how these dynamic features arise mechanistically and their…
Dynamical balance of excitation and inhibition is usually invoked to explain the irregular low firing activity observed in the cortex. We propose a robust nonlinear balancing mechanism for a random network of spiking neurons, which works…
The human brain is a complex dynamical system which displays a wide range of macroscopic and mesoscopic patterns of neural activity, whose mechanistic origin remains poorly understood. Whole-brain modelling allows us to explore candidate…
Many natural systems are organized as networks, in which the nodes (be they cells, individuals or populations) interact in a time-dependent fashion. The dynamic behavior of these networks depends on how these nodes are connected, which can…
We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular…