| Issue |
E3S Web Conf.
Volume 269, 2021
2021 International Conference on Environmental Engineering, Agricultural Pollution and Hydraulical Studies (EEAPHS 2021)
|
|
|---|---|---|
| Article Number | 01004 | |
| Number of page(s) | 8 | |
| Section | Environmental Engineering | |
| DOI | https://doi.org/10.1051/e3sconf/202126901004 | |
| Published online | 09 June 2021 | |
Optimal control for a size-structured predator-prey model in a polluted environment
1
School of Environmental and Municipal Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China
2
Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China
* Corresponding author: tn_zhang91@163.com
In this paper, we deal with an optimal harvesting problem for a periodic predator-prey hybrid system dependent on size-structure in a polluted environment. In other words, a size-dependent model in an environment with a small toxicant content has been established. The well-posedness of state system is proved by using the fixed point theorem. The necessary optimality conditions are derived by tangent-normal cone technique in nonlinear functional analysis. The existence of a unique optimal harvesting policy is verified via the Ekeland’s variational principle. The optimal harvesting problem has an optimal harvesting policy, which has a Bang-Bang structure and provides a threshold for the optimal harvesting problem. Using the optimization theories and methods in mathematics to control phenomena of life. The objective function represents the total economic profit from the harvested population. Some theoretical results obtained in this paper provide a scientific theoretical basis for the practical application of the model.
© The Authors, published by EDP Sciences, 2021
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