Stability of equilibriums and bifurcation analysis of two-dimensional autonomous competitive Lotka-Volterra dynamical system

Danijela Branković; Marija Mikić

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arXiv · 2410.18119

Stability of equilibriums and bifurcation analysis of two-dimensional autonomous competitive Lotka-Volterra dynamical system

Danijela Branković·Marija Mikić

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Abstract

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 $\mathrm{R}^2$.

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Danijela Branković, Marija Mikić. 2024-10-10. Stability of equilibriums and bifurcation analysis of two-dimensional autonomous competitive Lotka-Volterra dynamical system. https://arxiv.org/abs/2410.18119

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