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Volume 36, Issue 3
The Effect of Refuge and Proportional Harvesting for a Predator-Prey System with Reaction-Diffusion

Xueru Lin

Ann. Appl. Math., 36 (2020), pp. 235-247.

Published online: 2021-01

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  • Abstract

A diffusive predator-prey system with Holling-Tanner functional response and no-flux boundary condition is considered in this work. By using upper and lower solutions combined with iteration method, sufficient condition which ensures the global asymptotical stability of the unique positive equilibrium of the system is obtained. It is shown that the prey refuge and the proportional harvesting can influence the global asymptotical stability of unique positive equilibrium of the system, furthermore, they can change the position of the unique interior equilibrium and make species coexist more easily.

  • Keywords

reaction-diffusion system, iteration method, global asymptotical stability, prey refuge, proportional harvesting.

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COPYRIGHT: © Global Science Press

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@Article{AAM-36-235, author = {Lin , Xueru}, title = {The Effect of Refuge and Proportional Harvesting for a Predator-Prey System with Reaction-Diffusion}, journal = {Annals of Applied Mathematics}, year = {2021}, volume = {36}, number = {3}, pages = {235--247}, abstract = {

A diffusive predator-prey system with Holling-Tanner functional response and no-flux boundary condition is considered in this work. By using upper and lower solutions combined with iteration method, sufficient condition which ensures the global asymptotical stability of the unique positive equilibrium of the system is obtained. It is shown that the prey refuge and the proportional harvesting can influence the global asymptotical stability of unique positive equilibrium of the system, furthermore, they can change the position of the unique interior equilibrium and make species coexist more easily.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/18584.html} }
TY - JOUR T1 - The Effect of Refuge and Proportional Harvesting for a Predator-Prey System with Reaction-Diffusion AU - Lin , Xueru JO - Annals of Applied Mathematics VL - 3 SP - 235 EP - 247 PY - 2021 DA - 2021/01 SN - 36 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aam/18584.html KW - reaction-diffusion system, iteration method, global asymptotical stability, prey refuge, proportional harvesting. AB -

A diffusive predator-prey system with Holling-Tanner functional response and no-flux boundary condition is considered in this work. By using upper and lower solutions combined with iteration method, sufficient condition which ensures the global asymptotical stability of the unique positive equilibrium of the system is obtained. It is shown that the prey refuge and the proportional harvesting can influence the global asymptotical stability of unique positive equilibrium of the system, furthermore, they can change the position of the unique interior equilibrium and make species coexist more easily.

Xueru Lin. (2021). The Effect of Refuge and Proportional Harvesting for a Predator-Prey System with Reaction-Diffusion. Annals of Applied Mathematics. 36 (3). 235-247. doi:
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