JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (1): 77-88.doi: 10.6040/j.issn.1671-9352.0.2021.355

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Optimal harvesting for three species system with size-structures in periodic environments

ZHANG Hao, LUO Zhi-xue, ZHENG Xiu-juan   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2021-12-21

Abstract: The paper investigates the optimal harvesting for three-dimensional food chain model with size-structures in periodic environments. Firstly, by applying the theorem of Banach fixed point, we establish the existence and uniqueness of nonnegative bounded solutions. Secondly, we obtain the necessary conditions by using the tangent-normal cones. Finally, on the basis of Ekelands variational principle, we conclude that a unique optimal policy exists.

Key words: optimal harvesting, periodic environment, size-structure, Ekelands variational principle

CLC Number: 

  • O175.1
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