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Dynamical analysis on a size-structured population model of Daphnia with delayed birth process

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  • Hu, Dandan
  • Huang, Gang

Abstract

In this paper, we investigate a size-structured population model of Daphnia coupled with an unstructured algal food source. We introduce a delay into the boundary condition of this model, where the delay describes the effect of competition for finding food or resource in short supply juvenile period. Following the semigroup theory, we transform our model into the abstract boundary delay problem and obtain the existence and uniqueness of a positive stationary solution. By means of the spectral analysis and the characteristic equation technique, the instability and linear stability results of stationary solutions are formulated in terms of the basic reproduction number ℛ(F). Some numerical simulation examples are presented to illustrate the feasibility of our main results.

Suggested Citation

  • Hu, Dandan & Huang, Gang, 2022. "Dynamical analysis on a size-structured population model of Daphnia with delayed birth process," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s096007792200577x
    DOI: 10.1016/j.chaos.2022.112367
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    References listed on IDEAS

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    1. Wang, Jinliang & Wang, Jing & Kuniya, Toshikazu, 2019. "Analysis of an age-structured multi-group heroin epidemic model," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 78-100.
    2. Khan, Asaf & Zaman, Gul, 2018. "Global analysis of an age-structured SEIR endemic model," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 154-165.
    3. Wang, Sheng-Fu & Hu, Lin & Nie, Lin-Fei, 2021. "Global dynamics and optimal control of an age-structure Malaria transmission model with vaccination and relapse," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
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