Dynamics of solutions of a reaction-diffusion equation with delayed inhibition

Reaction-diffusion equation with a logistic production term and a delayed inhibition term is studied. Global stability of the homogeneous in space equilibrium is proved under some conditions on the delay term. In the case where these conditions are not satisfied, this solution can become unstable resulting in the emergence of spatiotemporal pattern formation studied in numerical simulations. © 2020 American Institute of Mathematical Sciences. All rights reserved.

Authors
Touaoula T.M.1 , Frioui M.N.1 , Bessonov N.2 , Volpert V. 3, 4, 5, 6
Journal
Discrete and Continuous Dynamical Systems - Series B
Publisher
Southwest Missouri State University
Number of issue
9
Language
English
Pages
2425-2442
Status
Published
Link
External link
DOI
10.3934/dcdss.2020193
Volume
13
Year
2020
Organizations
  • 1 Laboratoire d’Analyse Non linéaire et Mathématiques Appliquées, Département de Mathématiques, Université Aboubekr Belkaïd Tlemcen, Tlemcen, 13000, Algeria
  • 2 Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg, 199178, Russian Federation
  • 3 Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
  • 4 Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, Villeurbanne, 69622, France
  • 5 INRIA, Université de Lyon, Université Lyon 1, Institut Camille Jordan, 43 Bd. du 11 Novembre 1918, Villeurbanne Cedex, 69200, France
  • 6 Institute of Numerical Mathematics of the RAS, ul. Gubkina 8, Moscow, 119333, Russian Federation
Keywords
Delay reaction-diffusion equation; Global attractor; Pattern formation
Date of creation
02.11.2020
Date of change
02.11.2020
Short link
https://repository.rudn.ru/en/records/article/record/64462/
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