Delay reaction-diffusion equation for infection dynamics

Nonlinear dynamics of a reaction-diffusion equation with delay is studied with numerical simulations in 1D and 2D cases. Homogeneous in space solutions can manifest time oscillations with period doubling bifurcations and transition to chaos. Transition between two regions with homogeneous oscillations is provided by quasi-waves, propagating solutions without regular structure and often with complex aperiodic oscillations. Dynamics of space dependent solutions is described by a combination of various waves, e.g., bistable, monostable, periodic and quasi-waves. © 2019 American Institute of Mathematical Sciences. All Rights Reserved.

Authors
Bessonov N.1, 2 , Bocharov G. 2 , Touaoula T.M.3 , Trofimchuk S.4 , Volpert V. 2, 5, 6, 7
Journal
Discrete and Continuous Dynamical Systems - Series B
Publisher
Southwest Missouri State University
Number of issue
5
Language
English
Pages
2073-2091
Status
Published
Link
External link
DOI
10.3934/dcdsb.2019085
Volume
24
Year
2019
Organizations
  • 1 Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg, 199178, Russian Federation
  • 2 Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, Gubkina Street 8, Moscow, 119333, Russian Federation
  • 3 Département de Mathématiques, Faculté des Sciences, Université de Tlemcen Laboratoire d’Analyse Non Linéaire et Mathématiques Appliquées Tlemcen, BP 11913000, Algeria
  • 4 Instituto de Matemática y Fisica, Universidad de Talca, Casilla 747, Talca, Chile
  • 5 Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, Villeurbanne, 69622, France
  • 6 INRIA Team Dracula, INRIA Lyon La Doua, Villeurbanne, 69603, France
  • 7 RUDN University, ul. Miklukho-Maklaya 6, Moscow, 117198, Russian Federation
Keywords
Delay reaction-diffusion equation; Nonlinear dynamics; Wave propagation
Date of creation
19.07.2019
Date of change
19.07.2019
Short link
https://repository.rudn.ru/en/records/article/record/38664/
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