Optimal harvesting in a unidirectional consumer–resource mutualisms system with size structure in the consumer
This paper considers the optimal harvesting problem for a size-structured model of unidirectional consumer–resource mutualisms in which the consumer species has both positive and negative effects on the resource species, while the resource has only a positive effect on the consumer. First, we show...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2022-02-01
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| Series: | Nonlinear Analysis |
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| Online Access: | https://www.journals.vu.lt/nonlinear-analysis/article/view/26314 |
| _version_ | 1819049296473882624 |
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| author | Rong Liu Guirong Liu |
| author_facet | Rong Liu Guirong Liu |
| author_sort | Rong Liu |
| collection | DOAJ |
| description |
This paper considers the optimal harvesting problem for a size-structured model of unidirectional consumer–resource mutualisms in which the consumer species has both positive and negative effects on the resource species, while the resource has only a positive effect on the consumer. First, we show the existence of a unique nonnegative solution of the system and give the continuous dependence of solutions on the control variable. Next, the adjoint system is derived, which is necessary for optimality and the existence of a unique optimal policy. Then necessary conditions for optimality are established via the normal cone and adjoint system. Moreover, the existence of a unique optimal strategy is proved via Ekeland’s variational principle and fixed-point reasoning in convex analysis. Finally, we use numerical simulations to verify the main results and find other dynamic properties of the system.
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| first_indexed | 2024-12-21T11:29:54Z |
| format | Article |
| id | doaj.art-c4c5befbd4dd4c81804098625e7e4240 |
| institution | Directory Open Access Journal |
| issn | 1392-5113 2335-8963 |
| language | English |
| last_indexed | 2024-12-21T11:29:54Z |
| publishDate | 2022-02-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj.art-c4c5befbd4dd4c81804098625e7e42402022-12-21T19:05:35ZengVilnius University PressNonlinear Analysis1392-51132335-89632022-02-012710.15388/namc.2022.27.26314Optimal harvesting in a unidirectional consumer–resource mutualisms system with size structure in the consumerRong Liu0Guirong Liu1Shanxi University of Finance and EconomicsShanxi University This paper considers the optimal harvesting problem for a size-structured model of unidirectional consumer–resource mutualisms in which the consumer species has both positive and negative effects on the resource species, while the resource has only a positive effect on the consumer. First, we show the existence of a unique nonnegative solution of the system and give the continuous dependence of solutions on the control variable. Next, the adjoint system is derived, which is necessary for optimality and the existence of a unique optimal policy. Then necessary conditions for optimality are established via the normal cone and adjoint system. Moreover, the existence of a unique optimal strategy is proved via Ekeland’s variational principle and fixed-point reasoning in convex analysis. Finally, we use numerical simulations to verify the main results and find other dynamic properties of the system. https://www.journals.vu.lt/nonlinear-analysis/article/view/26314consumer–resource interactionsize structureoptimal harvestingEkeland’s variational principle |
| spellingShingle | Rong Liu Guirong Liu Optimal harvesting in a unidirectional consumer–resource mutualisms system with size structure in the consumer Nonlinear Analysis consumer–resource interaction size structure optimal harvesting Ekeland’s variational principle |
| title | Optimal harvesting in a unidirectional consumer–resource mutualisms system with size structure in the consumer |
| title_full | Optimal harvesting in a unidirectional consumer–resource mutualisms system with size structure in the consumer |
| title_fullStr | Optimal harvesting in a unidirectional consumer–resource mutualisms system with size structure in the consumer |
| title_full_unstemmed | Optimal harvesting in a unidirectional consumer–resource mutualisms system with size structure in the consumer |
| title_short | Optimal harvesting in a unidirectional consumer–resource mutualisms system with size structure in the consumer |
| title_sort | optimal harvesting in a unidirectional consumer resource mutualisms system with size structure in the consumer |
| topic | consumer–resource interaction size structure optimal harvesting Ekeland’s variational principle |
| url | https://www.journals.vu.lt/nonlinear-analysis/article/view/26314 |
| work_keys_str_mv | AT rongliu optimalharvestinginaunidirectionalconsumerresourcemutualismssystemwithsizestructureintheconsumer AT guirongliu optimalharvestinginaunidirectionalconsumerresourcemutualismssystemwithsizestructureintheconsumer |