Optimal Contraception Control for a Nonlinear Vermin Population Model with Size-Structure

Liu, Rong; Liu, Guirong

doi:10.1007/s00245-017-9428-y

Cited by 5 publications

(1 citation statement)

References 24 publications

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“…Let us make some comments on the difference of our results and methods with those of closely related works. For the optimal control problems of size-structured population https://www.journals.vu.lt/nonlinear-analysis models, the authors in [15,17,18] proved that the optimization problems admit at least one solution but paid no attention to the uniqueness. In addition, the structure of the optimal strategy did not considered in [15].…”

Section: Discussionmentioning

confidence: 99%

Optimal harvesting in a unidirectional consumer–resource mutualisms system with size structure in the consumer

Liu

2022

NAMC

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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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Section: Discussionmentioning

confidence: 99%

Optimal harvesting in a unidirectional consumer–resource mutualisms system with size structure in the consumer

Liu

2022

NAMC

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Optimal Contraception Control Problems in a Nonlinear Size-Structured Vermin Model

Liu

Zhang

Chen

2023

J Optim Theory Appl

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Optimal harvesting for a periodic competing system with size structure in a polluted environment

Zhang

Luo

2022

MATH

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<abstract><p>As a renewable resource, biological population not only has direct economic value to people's lives, but also has important ecological and environmental value. This study examines an optimal harvesting problem for a periodic, competing hybrid system of three species that is dependent on size structure in a polluted environment. The existence and uniqueness of the nonnegative solution are proved via an operator theory and fixed point theorem. The necessary optimality conditions are derived by constructing an adjoint system and using the tangent-normal cone technique. The existence of unique optimal control pair is verified by means of the Ekeland variational principle and a feedback form of the optimal policy is presented. The finite difference scheme and the chasing method are used to approximate the nonnegative T-periodic solution of the state system corresponding to a given initial datum. The objective functional represents the total profit obtained from harvesting three species. The results obtained in this work can be extended to a wide variety of fields.</p></abstract>

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Optimal Contraception Control for a Nonlinear Vermin Population Model with Size-Structure

Cited by 5 publications

References 24 publications

Optimal harvesting in a unidirectional consumer–resource mutualisms system with size structure in the consumer

Optimal harvesting in a unidirectional consumer–resource mutualisms system with size structure in the consumer

Optimal Contraception Control Problems in a Nonlinear Size-Structured Vermin Model

Optimal harvesting for a periodic competing system with size structure in a polluted environment

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