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

Meilin He (), Mingjue Zhu, Xuyang Teng, Zhirui Hu, Wei Feng, Huina Song, Xiyuan Chen and Haiquan Wang
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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

Mathematics, 2023, vol. 11, issue 20, 1-12

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.

Keywords: single species; global asymptotic stability; fixed points; Liapunov function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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