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A Stochastic Impulse Control Model for Population Management of Fish-Eating Bird Phalacrocorax Carbo and Its Numerical Computation

  • Yuta YaegashiEmail author
  • Hidekazu Yoshioka
  • Koichi Unami
  • Masayuki Fujihara
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 946)

Abstract

Feeding damage from a fish-eating bird Phalacrocorax carbo to a fish Plecoglossus altivelis is severe in Japan. A stochastic impulse control model is introduced for finding the cost-effective and ecologically conscious population management policy of the bird. The optimal management policy is of a threshold type; if the population reaches an upper threshold, then taking a countermeasure to immediately reduce the bird to a lower threshold. This optimal policy is found through solving a Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI). We propose a numerical method for HJBQVIs based on a policy iteration approach. Its accuracy on numerical solutions and the associated free boundaries for the management thresholds of the population, is investigated against an exact solution. The computational results indicate that the proposed numerical scheme can successfully solve the HJBQVI with the first-order computational accuracy. In addition, it is shown that the scheme captures the free boundaries subject to errors smaller than element lengths.

Keywords

Population management Impulse control Hamilton-Jacobi-Bellman quasi-variational inequality 

Notes

Acknowledgments

This paper is partly funded by grants-in-aid for scientific research No.16KT0018, No.17J09125, and No.17K15345 from the Japan Society for the Promotion of Science (JSPS).

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Yuta Yaegashi
    • 1
    • 2
    Email author
  • Hidekazu Yoshioka
    • 3
  • Koichi Unami
    • 1
  • Masayuki Fujihara
    • 1
  1. 1.Kyoto UniversityKyotoJapan
  2. 2.Research Fellow of Japan Society for the Promotion of ScienceTokyoJapan
  3. 3.Shimane UniversityMatsueJapan

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