Volume 34, Issue 2
Dynamical Analysis of a Single-Species Population Model with Migrations and Harvest Between Patches

Chenjia Wang & Fengying Wei

Ann. Appl. Math., 34 (2018), pp. 183-198.

Published online: 2022-06

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  • Abstract

A single-species population model with migrations and harvest between the protected patch and the unprotected patch is formulated and investigated in this paper. We study the local stability and the global stability of the equilibria. The research points out, under some suitable conditions, the single-species population model admits a unique positive equilibrium, which is globally asymptotically stable. We also derive that the trivial solution is globally asymptotically stable when the harvesting rate exceeds the threshold. Further, we discuss the practical effects of the protection zones and the harvest. The main results indicate that the protective zones indeed eliminate the extinction of the species under some cases, and the theoretical threshold of harvest to the practical management of the endangered species is provided as well. To end this contribution and to check the validity of the main results, numerical simulations are separately carried out to illustrate these results.

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34D23

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COPYRIGHT: © Global Science Press

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@Article{AAM-34-183, author = {Wang , Chenjia and Wei , Fengying}, title = {Dynamical Analysis of a Single-Species Population Model with Migrations and Harvest Between Patches}, journal = {Annals of Applied Mathematics}, year = {2022}, volume = {34}, number = {2}, pages = {183--198}, abstract = {

A single-species population model with migrations and harvest between the protected patch and the unprotected patch is formulated and investigated in this paper. We study the local stability and the global stability of the equilibria. The research points out, under some suitable conditions, the single-species population model admits a unique positive equilibrium, which is globally asymptotically stable. We also derive that the trivial solution is globally asymptotically stable when the harvesting rate exceeds the threshold. Further, we discuss the practical effects of the protection zones and the harvest. The main results indicate that the protective zones indeed eliminate the extinction of the species under some cases, and the theoretical threshold of harvest to the practical management of the endangered species is provided as well. To end this contribution and to check the validity of the main results, numerical simulations are separately carried out to illustrate these results.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/20572.html} }
TY - JOUR T1 - Dynamical Analysis of a Single-Species Population Model with Migrations and Harvest Between Patches AU - Wang , Chenjia AU - Wei , Fengying JO - Annals of Applied Mathematics VL - 2 SP - 183 EP - 198 PY - 2022 DA - 2022/06 SN - 34 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aam/20572.html KW - protection zone, migrations, harvesting, extinction. AB -

A single-species population model with migrations and harvest between the protected patch and the unprotected patch is formulated and investigated in this paper. We study the local stability and the global stability of the equilibria. The research points out, under some suitable conditions, the single-species population model admits a unique positive equilibrium, which is globally asymptotically stable. We also derive that the trivial solution is globally asymptotically stable when the harvesting rate exceeds the threshold. Further, we discuss the practical effects of the protection zones and the harvest. The main results indicate that the protective zones indeed eliminate the extinction of the species under some cases, and the theoretical threshold of harvest to the practical management of the endangered species is provided as well. To end this contribution and to check the validity of the main results, numerical simulations are separately carried out to illustrate these results.

Chenjia Wang & Fengying Wei. (2022). Dynamical Analysis of a Single-Species Population Model with Migrations and Harvest Between Patches. Annals of Applied Mathematics. 34 (2). 183-198. doi:
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