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Global Asymptotic Stability Analysis of Fixed Points for a Density-Dependent Single-Species Population Growth Model

Author

Listed:
  • Meilin He

    (School of Communications Engineering, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Mingjue Zhu

    (School of Communications Engineering, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Xuyang Teng

    (School of Communications Engineering, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Zhirui Hu

    (School of Communications Engineering, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Wei Feng

    (School of Communications Engineering, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Huina Song

    (Space Information Research Institute, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Xiyuan Chen

    (School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Haiquan Wang

    (School of Communications Engineering, Hangzhou Dianzi University, Hangzhou 310018, China)

Abstract

In a density-dependent single-species population growth model, a simple method is proposed to explicitly and directly derive the analytic expressions of reliable regions for local and global asymptotic stability. Specifically, first, a reliable region Λ LAS is explicitly represented by solving the fixed point and utilizing the asymptotic stability criterion, over which the fixed point is locally asymptotically stable. Then, two types of auxiliary Liapunov functions are constructed, where the variation of the Liapunov function is decomposed into the product of two functions and is always negative at the non-equilibrium state. Finally, based on the Liapunov stability theorem, a closed-form expression of reliable region Λ GAS is obtained, where the fixed point is globally asymptotically stable in the sense that all the solutions tend to fixed point. Numerical results show that our analytic expressions of reliable regions are accurate for both local and global asymptotic stability.

Suggested Citation

  • Meilin He & Mingjue Zhu & Xuyang Teng & Zhirui Hu & Wei Feng & Huina Song & Xiyuan Chen & Haiquan Wang, 2023. "Global Asymptotic Stability Analysis of Fixed Points for a Density-Dependent Single-Species Population Growth Model," Mathematics, MDPI, vol. 11(20), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4345-:d:1263138
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    References listed on IDEAS

    as
    1. Osama Moaaz & Dimplekumar Chalishajar & Omar Bazighifan, 2019. "Some Qualitative Behavior of Solutions of General Class of Difference Equations," Mathematics, MDPI, vol. 7(7), pages 1-12, July.
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