Stability of equilibriums and bifurcation analysis of two-dimensional autonomous competitive Lotka-Volterra dynamical system
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909361565073408 |
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| author | Branković, Danijela Mikić, Marija |
| author_facet | Branković, Danijela Mikić, Marija |
| contents | A detailed analysis of the stability of equilibriums and bifurcations of the two-dimensional autonomous competitive Lotka-Volterra dynamical system is performed. Necessary and sufficient conditions are determined for equilibriums (without the origin) to be asymptotically stable or unstable on $\left[0, +\infty\right)^2$. Necessary and sufficient conditions are determined so that the observed dynamical system has no equilibriums in $\left(0, +\infty\right)^2 $. All results are presented in five tables and five figures. We also found that four transcritical bifurcations occur in the observed dynamical system if it is analyzed on $\mathrm{R}^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18119 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of equilibriums and bifurcation analysis of two-dimensional autonomous competitive Lotka-Volterra dynamical system Branković, Danijela Mikić, Marija General Mathematics 34A34, 34C23, 37C75 A detailed analysis of the stability of equilibriums and bifurcations of the two-dimensional autonomous competitive Lotka-Volterra dynamical system is performed. Necessary and sufficient conditions are determined for equilibriums (without the origin) to be asymptotically stable or unstable on $\left[0, +\infty\right)^2$. Necessary and sufficient conditions are determined so that the observed dynamical system has no equilibriums in $\left(0, +\infty\right)^2 $. All results are presented in five tables and five figures. We also found that four transcritical bifurcations occur in the observed dynamical system if it is analyzed on $\mathrm{R}^2$. |
| title | Stability of equilibriums and bifurcation analysis of two-dimensional autonomous competitive Lotka-Volterra dynamical system |
| topic | General Mathematics 34A34, 34C23, 37C75 |
| url | https://arxiv.org/abs/2410.18119 |