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Optimal control for a size-structured predator-prey model in a polluted environment
- Source :
- E3S Web of Conferences, Vol 269, p 01004 (2021)
- Publication Year :
- 2021
- Publisher :
- EDP Sciences, 2021.
-
Abstract
- 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.
- Subjects :
- 0303 health sciences
0209 industrial biotechnology
education.field_of_study
Mathematical optimization
Basis (linear algebra)
Population
Structure (category theory)
Fixed-point theorem
02 engineering and technology
Optimal control
Environmental sciences
03 medical and health sciences
020901 industrial engineering & automation
Variational principle
Hybrid system
Nonlinear functional analysis
GE1-350
education
030304 developmental biology
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 22671242
- Volume :
- 269
- Database :
- OpenAIRE
- Journal :
- E3S Web of Conferences
- Accession number :
- edsair.doi.dedup.....6c44f21b5da08cd0d9b10688574d0d57