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Global stability of stage-structured single species model on ℝN with Beverton–Holt birth function.

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Title: Global stability of stage-structured single species model on ℝN with Beverton–Holt birth function.
Authors: Zhang, Hongtao1 (AUTHOR), Zhao, Jingfu1 (AUTHOR) zhengqing1102@163.com
Source: Applied Mathematics in Science & Engineering. Dec2025, Vol. 33 Issue 1, p1-10. 10p.
Subjects: Cauchy problem, Elliptic equations, Life cycles (Biology), Population dynamics, Stability (Mechanics), Dynamical systems, Asymptotic expansions
Abstract: Our article discusses a Cauchy problem of a single species model with stage structure and Beverton–Holt birth function. The global stability of the Cauchy problem is completely surveyed by using the global stability of the corresponding elliptic system with Dirichlet condition. Firstly, appropriate upper and lower solutions for a system of elliptic equations are constructed to prove the existence and uniqueness of solutions. Then, utilizing the theory of monotonic dynamical systems to initial boundary value problem, the uniform convergence of solutions is given. Finally, the asymptotic behaviour of Cauchy problem solutions is discussed, and it is proved that the Cauchy problem solution converges to a constant equilibrium solution. [ABSTRACT FROM AUTHOR]
Copyright of Applied Mathematics in Science & Engineering is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Global stability of stage-structured single species model on ℝN with Beverton–Holt birth function.
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  Data: <searchLink fieldCode="AR" term="%22Zhang%2C+Hongtao%22">Zhang, Hongtao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhao%2C+Jingfu%22">Zhao, Jingfu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> zhengqing1102@163.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Applied+Mathematics+in+Science+%26+Engineering%22">Applied Mathematics in Science & Engineering</searchLink>. Dec2025, Vol. 33 Issue 1, p1-10. 10p.
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  Data: <searchLink fieldCode="DE" term="%22Cauchy+problem%22">Cauchy problem</searchLink><br /><searchLink fieldCode="DE" term="%22Elliptic+equations%22">Elliptic equations</searchLink><br /><searchLink fieldCode="DE" term="%22Life+cycles+%28Biology%29%22">Life cycles (Biology)</searchLink><br /><searchLink fieldCode="DE" term="%22Population+dynamics%22">Population dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+%28Mechanics%29%22">Stability (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Asymptotic+expansions%22">Asymptotic expansions</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Our article discusses a Cauchy problem of a single species model with stage structure and Beverton–Holt birth function. The global stability of the Cauchy problem is completely surveyed by using the global stability of the corresponding elliptic system with Dirichlet condition. Firstly, appropriate upper and lower solutions for a system of elliptic equations are constructed to prove the existence and uniqueness of solutions. Then, utilizing the theory of monotonic dynamical systems to initial boundary value problem, the uniform convergence of solutions is given. Finally, the asymptotic behaviour of Cauchy problem solutions is discussed, and it is proved that the Cauchy problem solution converges to a constant equilibrium solution. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Applied Mathematics in Science & Engineering is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1080/27690911.2025.2551358
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      – Code: eng
        Text: English
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        PageCount: 10
        StartPage: 1
    Subjects:
      – SubjectFull: Cauchy problem
        Type: general
      – SubjectFull: Elliptic equations
        Type: general
      – SubjectFull: Life cycles (Biology)
        Type: general
      – SubjectFull: Population dynamics
        Type: general
      – SubjectFull: Stability (Mechanics)
        Type: general
      – SubjectFull: Dynamical systems
        Type: general
      – SubjectFull: Asymptotic expansions
        Type: general
    Titles:
      – TitleFull: Global stability of stage-structured single species model on ℝN with Beverton–Holt birth function.
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            NameFull: Zhang, Hongtao
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            – D: 01
              M: 12
              Text: Dec2025
              Type: published
              Y: 2025
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            – TitleFull: Applied Mathematics in Science & Engineering
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