arXiv subjects

Q Weng

Publications and source records attributed to Q Weng.

3 recordsLinked to original sources

arXiv2016

Relaxation in time elapsed neuron network models in the weak connectivity regime

In order to describe the firing activity of a homogenous assembly of neurons, we consider time elapsed models, which give mathematical descriptions of the probability density of neurons structured by the distribution of times elapsed since the last discharge. Under general assumption on the firing rate and the delay distribution, we prove the uniqueness of the steady state and its nonlinear exponential stability in the weak connectivity regime. The result generalizes some similar results obtained in [10] in the case without delay. Our approach uses the spectral analysis theory for semigroups in Banach spaces developed recently by the first author and collaborators.

math.AP↗

arXiv2016

General time elapsed neuron network model: well-posedness and strong connectivity regime

For large fully connected neuron networks, we study the dynamics of homogenous assemblies of interacting neurons described by time elapsed models, indicating how the time elapsed since the last discharge construct the probability density of neurons. Through the spectral analysis theory for semigroups in Banach spaces developed recently in [6, 9], on the one hand, we prove the existence and the uniqueness of the weak solution in the whole connectivity regime as well as the parallel results on the long time behavior of solutions obtained in [10] under general assumptions on the ring rate and the delay distribution. On the other hand, we extend those similar results obtained in [11, 12] in the case without delay to the case taking delay into account and both in the weak and the strong connectivity regime with a particular step function ring rate. Our approach uses the spectral analysis theory for semigroups in Banach spaces developed recently by the first author and collaborators.

math.AP↗

arXiv2016

On a linear runs and tumbles equation

We consider a linear runs and tumbles equation in dimension d $\ge$ 1 for which we establish the existence of a unique positive and normalized steady state as well as its asymptotic stability, improving similar results obtained by Calvez et al. [5] in dimension d = 1. Our analysis is based on the Krein-Rutman theory revisited in [18] together with some new moment estimates for proving confinement mechanism as well as dispersion, multiplicator and averaging lemma arguments for proving some regularity property of suitable iterated averaging quantities.

math.AP↗