JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (4): 29-39.doi: 10.6040/j.issn.1671-9352.0.2024.168

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Sparse optimal control of a vegetation model with cross diffusion

LIANG Juan1, ZHANG Jinzhu1*, CUI Liang2   

  1. 1. Department of Science, Taiyuan Institute of Technology, Taiyuan 030008, Shanxi, China;
    2. College of Resources and Environment, Shanxi University of Finance and Economics, Taiyuan 030006, Shanxi, China
  • Published:2025-04-08

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Abstract: A vegetation-water reaction-diffusion model with cross diffusion is established and human activities are chosen as the control function. The sparse optimal control problem of the model is studied which reveals how to improve the robustness of the ecosystem through human activities from the perspective of controlling the formation of vegetation pattern. Firstly, the conditions for generating Turing pattern are given. Furthermore, the first order necessary optimality condition is derived. Finally, the rationality of the control method and the effectiveness of the control strategy are verified in terms of the control effect, control error and control cost by numerical simulations.

Key words: vegetation pattern, desertification, robustness, optimal control, sparse control

CLC Number: 

  • O175
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