Optimal harvesting of an abstract population model with interval biological parameters

Advances in Difference Equations

article

Huang, Lirong¹  Cai, Donghan¹  Liu, Weiyi² 

[1] School of Mathematics and Statistics, Wuhan University;School of Information Engineering, Guizhou University of Traditional Chinese Medicine

关键词: Marine protected area;    Abstract model;    Interval-valued function;    Bionomic equilibrium;    Optimal control;    Current Hamiltonian function;   

DOI  :  10.1186/s13662-020-02755-1

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

We study the optimal harvesting policy for fishery in the marine protected and unreserved areas. In the literature, it is generally assumed that the fish population follows a concrete growth law. In contrast, we consider an abstract model with migration from the reserved area to the unreserved one. Then we examine and analyze the existence and stability of a nontrivial equilibrium point of the model. We also discuss the bionomic equilibrium. After that, we use the Pontryagin maximum principle to obtain the optimal harvest policy, where, instead of the well-known Hamiltonian function, we use the current Hamiltonian function to ease the calculation. Finally, we give some numerical examples to further illustrate our statements, where we also find that in practice the impreciseness of the parameters can influence the existence of the system positive equilibrium.

【 授权许可】

CC BY