Open AccessA consumer-resource competition model with a state-dependent delay and stage-structured consumer species
Author(s) -
Yan Wang,
Xiaoning Liu,
Yang Jiang Wei
Publication year - 2020
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2020322
Subject(s) - uniqueness , maturity (psychological) , competition (biology) , resource (disambiguation) , competition model , stage (stratigraphy) , mathematics , term (time) , mathematical economics , econometrics , computer science , economics , mathematical optimization , microeconomics , ecology , physics , geology , mathematical analysis , biology , psychology , profit (economics) , developmental psychology , computer network , paleontology , quantum mechanics
In this paper, a new consumer-resource competition model with a state-dependent maturity delay is developed, which incorporates one resource species and two stage-structured consumer species. The main innovation is that the model directly manifests the relationship between resources and maturity time of consumers through a correction term, $1-\tau'(x(t))x'(t)$. Firstly, the well-posedness of the solution is studied. At the same time, the existence and uniqueness of all equilibria are discussed. Then, the linearized stabilities of the equilibria are achieved. Finally, some sufficient conditions which ensure the global attractivity of the coexistence equilibrium are obtained.