التفاصيل البيبلوغرافية
| العنوان: |
Long time behavior of an age and leaky memory-structured neuronal population equation |
| المؤلفون: |
Fonte Sanchez, Claudia, Schmutz, Valentin |
| سنة النشر: |
2023 |
| المجموعة: |
Base Institutionnelle de Recherche de l'université Paris-Dauphine (BIRD) |
| مصطلحات موضوعية: |
long time behavior, nonlocal transport equation, mean-field equation, Doeblin's and Harris's theorems, piecewise deterministic Markov process, spiking neuron, spike-frequency adaptation, short-term synaptic plasticity, Analyse |
| الوقت: |
515 |
| الوصف: |
We study the asymptotic stability of a two-dimensional mean-field neuronal population equation, which is explicitly linked to spiking neuron models, and generalizes the time-elapsed neuron network model by the inclusion of a leaky memory variable. This additional variable can represent a slow fatigue mechanism, like spike frequency adaptation or short-term synaptic depression. Even though two-dimensional models are known to have emergent behaviors, like population bursts, which are not observed in one-dimensional models, we show that in the weak connectivity regime, two-dimensional models behave like one-dimensional models, i.e. they relax to a unique stationary state. The proof is based on a version of Harris' ergodic theorem and a perturbation argument. The multidimensionality of the model and delay effects require careful consideration. ; non ; non ; recherche ; International |
| نوع الوثيقة: |
article in journal/newspaper |
| وصف الملف: |
application/pdf |
| اللغة: |
English |
| تدمد: |
0036-1410 |
| العلاقة: |
SIAM Journal on Mathematical Analysis; 54; 2022; 34; SIAM - Society for Industrial and Applied Mathematics; oui; https://basepub.dauphine.psl.eu/handle/123456789/22363Test |
| الإتاحة: |
https://basepub.dauphine.psl.eu/handle/123456789/22363Test |
| رقم الانضمام: |
edsbas.9D24DB32 |
| قاعدة البيانات: |
BASE |
