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. |
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| 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] |
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| Database: | Engineering Source |
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| 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] |
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| ISSN: | 27690911 |
| DOI: | 10.1080/27690911.2025.2551358 |
