| Autor: |
Orlando Merino, J. Marcotte, Mustafa R. S. Kulenović |
| Rok vydání: |
2021 |
| Předmět: |
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| Zdroj: |
Discrete & Continuous Dynamical Systems - B. 26:2721 |
| ISSN: |
1553-524X |
| DOI: |
10.3934/dcdsb.2020202 |
| Popis: |
It is shown that locally asymptotically stable equilibria of planar cooperative or competitive maps have basin of attraction \begin{document}$ \mathcal{B} $\end{document} with relatively simple geometry: the boundary of each component of \begin{document}$ \mathcal{B} $\end{document} consists of the union of two unordered curves, and the components of \begin{document}$ \mathcal{B} $\end{document} are not comparable as sets. The boundary curves are Lipschitz if the map is of class \begin{document}$ C^1 $\end{document} . Further, if a periodic point is in \begin{document}$ \partial \mathcal{B} $\end{document} , then \begin{document}$ \partial\mathcal{B} $\end{document} is tangential to the line through the point with direction given by the eigenvector associated with the smaller characteristic value of the map at the point. Examples are given. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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