相关论文: Asymptotic behaviour of neuron population models s…
We analyze the dynamics of two coupled identical populations of quadratic integrate-and-fire neurons, which represent the canonical model for class I neurons near the spiking threshold. The populations are heterogeneous; they include both…
We consider the influence of local noise on a generalized network of populations having positive and negative feedbacks. The population dynamics at the nodes is nonlinear, typically chaotic, and allows cessation of activity if the…
Recently, the distributed state estimation problem for continuous-time linear systems over jointly connected switching networks was solved. It was shown that the estimation errors will asymptotically converge to the origin by using the…
A nonlinear time-delay model is proposed to describe the interaction dynamics between criminal and non-criminal populations, combining social influence mechanisms, saturation effects represented by a Holling type II functional response, and…
We introduce a nonlinear structured population model with diffusion in the state space. Individuals are structured with respect to a continuous variable which represents a pathogen load. The class of uninfected individuals constitutes a…
An amenable, analytical two-state description of the nonlinear population dynamics of a noisy bistable system driven by a rectangular subthreshold signal is put forward. Explicit expressions for the driven population dynamics, the…
A lecture notes style review of the equilibrium statistical mechanics of recurrent neural networks with discrete and continuous neurons (e.g. Ising, coupled-oscillators). To be published in the Handbook of Biological Physics…
Cortical activity in-vivo displays relaxational time scales much longer than the membrane time constant of the neurons or the deactivation time of ionotropic synaptic conductances. The mechanisms responsible for such slow dynamics are not…
We investigate numerically the collective dynamical behavior of pulse-coupled non-leaky integrate-and-fire-neurons that are arranged on a two-dimensional small-world network. To ensure ongoing activity, we impose a probability for…
Inspired by language competition processes, we present a model of coupled evolution of node and link states. In particular, we focus on the interplay between the use of a language and the preference or attitude of the speakers towards it,…
The dynamical properties of a diluted fully-inhibitory network of pulse-coupled neurons are investigated. Depending on the coupling strength, two different phases can be observed. At low coupling the evolution rapidly converges towards…
We study a stochastic system of interacting neurons and its metastable properties. The system consists of $N$ neurons, each spiking randomly with rate depending on its membrane potential. At its spiking time, the neuron potential is reset…
Effective connectivity analysis provides an understanding of the functional organization of the brain by studying how activated regions influence one other. We propose a nonparametric Bayesian approach to model effective connectivity…
Stochastic dynamic models have been extensively used for the description of processes with uncertainties arising in the operations research, behavioral sciences, and many other application areas. A large class of the problems from these…
Contemporary neuroscience has embraced network science to study the complex and self-organized structure of the human brain; one of the main outstanding issues is that of inferring from measure data, chiefly functional Magnetic Resonance…
Networks observed in real world like social networks, collaboration networks etc., exhibit temporal dynamics, i.e. nodes and edges appear and/or disappear over time. In this paper, we propose a generative, latent space based, statistical…
We begin by demonstrating that the neuronal state equation from Dynamic Causal Modelling takes on the form of the discretized Fokker-Planck equation upon the inclusion of local activity gradients within a network. Using the Jacobian of this…
Neural population activity relating to behaviour is assumed to be inherently low-dimensional despite the observed high dimensionality of data recorded using multi-electrode arrays. Therefore, predicting behaviour from neural population…
Cortical neurons whose activity is recorded in behavioral experiments has been classified into several types such as stimulus-related neurons, delay-period neurons, and reward-related neurons. Moreover, the population activity of neurons…
A significant proportion of the infections driving the current {SARS-CoV-2} pandemic are transmitted asymptomatically. Here we introduce and study a simple epidemic model with separate compartments comprising asymptomatic and symptomatic…