On classification of a 4D competitive LV system
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- by Wenxi Wu and Jifa Jiang;
- Proc. Amer. Math. Soc. 152 (2024), 1983-1997
- DOI: https://doi.org/10.1090/proc/16601
- Published electronically: March 1, 2024
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Abstract:
This paper classifies the global dynamics of a 4D competitive Lotka-Volterra system (1.3) with two positive parameters $k_1,\ k_2$ via carrying simplex. It is proved that the interior of the carrying simplex is filled with periodic orbits except equilibria and each interior trajectory is persistent and tends to either a periodic orbit or an equilibrium if $k_1/k_2=2$. Otherwise, the system admits two 2D carrying simplices $\Delta _i$ on $x_1=i$ for $i=0,\ 1$, which are filled with periodic orbits surrounding an equilibrium. All interior orbits go in the long run to $\Delta _1$ if $k_1/k_2>2$. If $0<k_1/k_2<2$, then the system admits a bistable structure: $\Delta _0$ and the equilibrium $R_1(1+k_2/k_1,\ 0,\ 0,\ 0)$ are locally asymptotically stable, the attracting set of $\Delta _1$ separates the attracting basins of $\Delta _0$ and $R_1$.References
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Bibliographic Information
- Wenxi Wu
- Affiliation: Mathematics and Science College, Shanghai Normal University, Shanghai 200234, People’s Republic of China
- ORCID: 0000-0002-4590-0729
- Email: jiangjf@shnu.edu.cn
- Jifa Jiang
- ORCID: 0000-0002-4590-0729
- Received by editor(s): February 21, 2023
- Received by editor(s) in revised form: May 22, 2023
- Published electronically: March 1, 2024
- Additional Notes: This work was supported by the National Natural Science Foundation of China (NSFC) under Grant Nos. 12171321.
- Communicated by: Wenxian Shen
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 1983-1997
- MSC (2020): Primary 34C12, 34D09, 37C65, 37C70
- DOI: https://doi.org/10.1090/proc/16601
- MathSciNet review: 4728468