JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (11): 51-60.doi: 10.6040/j.issn.1671-9352.0.2021.140

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Optimal control of nonlinear competing populations based on the size-structure

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

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2021-11-15

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Abstract: The optimal control of nonlinear competing population systems based on the size-structure is studied in this paper. Firstly, the existence and uniqueness of separable form solutions are proved by using the method of characteristic lines and the fixed point theorem. Then, the adjoint system is derived. Finally, the optimal control of Bang-Bang type and the necessary condition of optimal control are given by using the concept of tangent and normal cones.

Key words: size-structure, competitive population, adjoint system, optimal control

CLC Number: 

  • O175.1
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