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A consumer-resource competition model with a state-dependent delay and stage-structured consumer species

1 Key Laboratory of Eco-environments in Three Gorges Reservoir Region (Ministry of Education), School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
2 School of Mathematics and Statistics, Nanning Normal University, Nanning 530023, China

Special Issues: Applications of delay differential equations in biology

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.
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Keywords competition model; state-dependent maturity delay; stability; global attractivity

Citation: Yan Wang, Xianning Liu, Yangjiang Wei. A consumer-resource competition model with a state-dependent delay and stage-structured consumer species. Mathematical Biosciences and Engineering, 2020, 17(5): 6064-6084. doi: 10.3934/mbe.2020322

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