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Global Stabilization of a Single-Species Ecosystem with Markovian Jumping under Neumann Boundary Value via Laplacian Semigroup

Author

Listed:
  • Ruofeng Rao

    (Department of Mathematics, Chengdu Normal University, Chengdu 611130, China)

  • Jialin Huang

    (Department of Mathematics, Sichuan Sanhe Vocational College, Luzhou 646200, China)

  • Xinsong Yang

    (College of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China)

Abstract

By applying impulsive control, this work investigated the global stabilization of a single-species ecosystem with Markovian jumping, a time delay and a Neumann boundary condition. Variational methods, a fixed-point theorem, and Laplacian semigroup theory were employed to derive the unique existence of the global stable equilibrium point, which is a positive number. Numerical examples illuminate the feasibility of the proposed methods.

Suggested Citation

  • Ruofeng Rao & Jialin Huang & Xinsong Yang, 2021. "Global Stabilization of a Single-Species Ecosystem with Markovian Jumping under Neumann Boundary Value via Laplacian Semigroup," Mathematics, MDPI, vol. 9(19), pages 1-11, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2446-:d:648571
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    References listed on IDEAS

    as
    1. Rao, Ruofeng & Yang, Xinsong & Tang, Rongqiang & Zhang, Yulin & Li, Xinggui & Shi, Lei, 2021. "Impulsive stabilization and stability analysis for Gilpin–Ayala competition model involved in harmful species via LMI approach and variational methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 571-590.
    2. Feng, Yuming & Yang, Xinsong & Song, Qiang & Cao, Jinde, 2018. "Synchronization of memristive neural networks with mixed delays via quantized intermittent control," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 874-887.
    3. Ruofeng Rao & Quanxin Zhu & Jialin Huang & Eulalia Mart nez, 2021. "Existence, Uniqueness, and Input-to-State Stability of Ground State Stationary Strong Solution of a Single-Species Model via Mountain Pass Lemma," Complexity, Hindawi, vol. 2021, pages 1-11, April.
    4. Ji, Weiming & Hu, Guixin, 2021. "Stability and explicit stationary density of a stochastic single-species model," Applied Mathematics and Computation, Elsevier, vol. 390(C).
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    Cited by:

    1. Khalid A. Alattas & Ardashir Mohammadzadeh & Saleh Mobayen & Hala M. Abo-Dief & Abdullah K. Alanazi & Mai The Vu & Arthur Chang, 2022. "Automatic Control for Time Delay Markov Jump Systems under Polytopic Uncertainties," Mathematics, MDPI, vol. 10(2), pages 1-18, January.

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