| Title: |
Dynamics of Periodic Waves in a Neural Field Model |
| Authors: |
Bessonov, Nikolai; Beuter, Anne; Trofimchuk, Sergei; Volpert, Vitaly |
| Contributors: |
Institute for Problems of Mechanical Engineering (IPME RAS); Russian Academy of Sciences Moscow (RAS); Institut Polytechnique de Bordeaux (Bordeaux INP); CorStim SAS Montpellier; Instituto de Matemática y Física - Universidad de Talca; Universidad de Talca; Institut Camille Jordan (ICJ); École Centrale de Lyon (ECL); Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL); Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon); Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS); Multi-scale modelling of cell dynamics : application to hematopoiesis (DRACULA); Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC); Université Claude Bernard Lyon 1 (UCBL); Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL); Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Centre Inria de l'Université Grenoble Alpes; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan (ICJ); Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL); Modélisation mathématique, calcul scientifique (MMCS) |
| Source: |
ISSN: 2227-7390 ; Mathematics ; https://hal.science/hal-03027337 ; Mathematics , 2020, 8 (7), pp.1-17. ⟨10.3390/math8071076⟩. |
| Publisher Information: |
CCSD; MDPI |
| Publication Year: |
2020 |
| Collection: |
Université Jean Monnet – Saint-Etienne: HAL |
| Subject Terms: |
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] |
| Description: |
International audience ; Periodic traveling waves are observed in various brain activities, including visual, motor, language, sleep, and so on. There are several neural field models describing periodic waves assuming nonlocal interaction, and possibly, inhibition, time delay or some other properties. In this work we study the influences of asymmetric connectivity functions and of time delay for symmetric connectivity functions on the emergence of periodic waves and their properties. Nonlinear wave dynamics are studied, including modulated and aperiodic waves. Multiplicity of waves for the same values of parameters is observed. External stimulation in order to restore wave propagation in a damaged tissue is discussed. |
| Document Type: |
article in journal/newspaper |
| Language: |
English |
| DOI: |
10.3390/math8071076 |
| Availability: |
https://hal.science/hal-03027337; https://hal.science/hal-03027337v1/document; https://hal.science/hal-03027337v1/file/mathematics-08-01076-v2.pdf; https://doi.org/10.3390/math8071076 |
| Rights: |
info:eu-repo/semantics/OpenAccess |
| Accession Number: |
edsbas.DBC42A94 |
| Database: |
BASE |