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Optimization of a Prey–Predator Model with Hysteresis and Convection

Author

Listed:
  • Chen Bin

    (Huaqiao University)

  • Xiao Yu Liang

    (Huaqiao University)

  • Emil Minchev

    (Hikari Ltd)

  • Sergey A. Timoshin

    (Huaqiao University
    Russian Academy of Sciences)

Abstract

A nonconvex optimal control problem for a partial differential system is proposed and analyzed. Our nonlinear control system can be interpreted in the population dynamics framework when, along with diffusional, hysteretic and migratory effects in the evolution of biological species are accounted for. We prove the existence of a nearly optimal solution to the optimization problem through relaxation-type properties; we establish for the underlying minimizing cost functional and control system.

Suggested Citation

  • Chen Bin & Xiao Yu Liang & Emil Minchev & Sergey A. Timoshin, 2023. "Optimization of a Prey–Predator Model with Hysteresis and Convection," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 347-371, July.
    • Handle: RePEc:spr:joptap:v:198:y:2023:i:1:d:10.1007_s10957-023-02225-0
    DOI: 10.1007/s10957-023-02225-0
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    References listed on IDEAS

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    1. Amar Debbouche & Juan J. Nieto & Delfim F. M. Torres, 2017. "Optimal Solutions to Relaxation in Multiple Control Problems of Sobolev Type with Nonlocal Nonlinear Fractional Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 7-31, July.
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