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Further Studies on the Dynamics of a Lotka–Volterra Competitor–Competitor–Mutualist System with Time-Varying Delays

Author

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  • Liang Cao

    (College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
    The Key Laboratory of Applied Mathematics of Xinjiang, Xinjiang University, Urumqi 830017, China
    These authors contributed equally to this work.)

  • Azhar Halik

    (College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
    These authors contributed equally to this work.)

  • Ahmadjan Muhammadhaji

    (College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
    The Key Laboratory of Applied Mathematics of Xinjiang, Xinjiang University, Urumqi 830017, China)

Abstract

In this paper, a Lotka–Volterra (L-V) competitor–competitor–mutualist system with time-varying delays is studied. Some dynamical behaviors of the considered system are investigated. Firstly, we obtain the boundedness, permanence and periodic solution of the system using the comparison principle of differential equations and inequality estimation method. Then, the global attractiveness of the system is analyzed by multiple Lyapunov functionals. Meanwhile, the existence and global attractivity of positive periodic solutions is derived. In the third section, in order to validate the practicability and feasibility of the obtained theoretical results, we conducted numerical simulations using MATLAB function ddesd . Finally, the fourth section is where conclusions are drawn.

Suggested Citation

  • Liang Cao & Azhar Halik & Ahmadjan Muhammadhaji, 2023. "Further Studies on the Dynamics of a Lotka–Volterra Competitor–Competitor–Mutualist System with Time-Varying Delays," Mathematics, MDPI, vol. 11(13), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2902-:d:1181988
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    References listed on IDEAS

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    1. Liu, Ruifen & Ma, Wenjin & Zeng, Jiakui & Zeng, Chunhua, 2019. "Double stochastic resonance in an insect ecosystem with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 563-576.
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    3. Du, Wentong & Xiao, Min & Ding, Jie & Yao, Yi & Wang, Zhengxin & Yang, Xinsong, 2023. "Fractional-order PD control at Hopf bifurcation in a delayed predator–prey system with trans-species infectious diseases," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 414-438.
    4. Castillo-Alvino, Hamlet Humberto & Marvá, Marcos, 2022. "Group defense promotes coexistence in interference competition: The Holling type IV competitive response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 426-445.
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