Optimal harvesting in a unidirectional consumer–resource mutualisms system with size structure in the consumer
Articles
Rong Liu
Shanxi University of Finance and Economics
https://orcid.org/0000-0003-2853-1949
Guirong Liu
Shanxi University
https://orcid.org/0000-0001-9362-5859
Published 2022-03-01
https://doi.org/10.15388/namc.2022.27.26314
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Keywords

consumer–resource interaction
size structure
optimal harvesting
Ekeland’s variational principle

How to Cite

Liu, R. and Liu, G. (2022) “Optimal harvesting in a unidirectional consumer–resource mutualisms system with size structure in the consumer”, Nonlinear Analysis: Modelling and Control, 27(2), pp. 385–411. doi:10.15388/namc.2022.27.26314.

Abstract

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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