Open AccessAn analysis approach to permanence of a delay differential equations model of microorganism flocculation
Author(s) -
Shuaiqi Guo,
Jinǵan Cui,
Wanbiao Ma
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021208
Subject(s) - monotonic function , flocculation , mathematics , differential equation , comparison theorem , microorganism , function (biology) , persistence (discontinuity) , differential (mechanical device) , mathematical economics , mathematical analysis , thermodynamics , environmental engineering , environmental science , biology , physics , geology , geotechnical engineering , evolutionary biology , bacteria , genetics
In this paper, we develop a delay differential equations model of microorganism flocculation with general monotonic functional responses, and then study the permanence of this model, which can ensure the sustainability of the collection of microorganisms. For a general differential system, the existence of a positive equilibrium can be obtained with the help of the persistence theory, whereas we give the existence conditions of a positive equilibrium by using the implicit function theorem. Then to obtain an explicit formula for the ultimate lower bound of microorganism concentration, we propose a general analysis method, which is different from the traditional approaches in persistence theory and also extends the analysis techniques of existing related works.