Open AccessTraveling waves in delayed reaction-diffusion equations in biology
Author(s) -
Sergeĭ Trofimchuk,
Vitaly Volpert
Publication year - 2020
Publication title -
mathematical biosciences and engineering
Language(s) - Uncategorized
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2020339
Subject(s) - monotonic function , traveling wave , reaction–diffusion system , stability (learning theory) , wavefront , mathematics , mathematical analysis , mathematical and theoretical biology , calculus (dental) , physics , computer science , optics , biology , medicine , dentistry , machine learning , genetics
This paper represents a literature review on traveling waves described by delayed reactiondiffusion (RD, for short) equations. It begins with the presentation of different types of equations arising in applications. The main results on wave existence and stability are presented for the equations satisfying the monotonicity condition that provides the applicability of the maximum and comparison principles. Other methods and results are described for the case where the monotonicity condition is not satisfied. The last two sections deal with delayed RD equations in mathematical immunology and in neuroscience. Existence, stability, and dynamics of wavefronts and of periodic waves are discussed.