| Autor: |
Daniel S. Graça, Ning Zhong |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
Logical Methods in Computer Science, Vol Volume 20, Issue 2 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
1860-5974 |
| DOI: |
10.46298/lmcs-20(2:19)2024 |
| Popis: |
In this paper, we examine the relationship between the stability of the dynamical system $x^{\prime}=f(x)$ and the computability of its basins of attraction. We present a computable $C^{\infty}$ system $x^{\prime}=f(x)$ that possesses a computable and stable equilibrium point, yet whose basin of attraction is robustly non-computable in a neighborhood of $f$ in the sense that both the equilibrium point and the non-computability of its associated basin of attraction persist when $f$ is slightly perturbed. This indicates that local stability near a stable equilibrium point alone is insufficient to guarantee the computability of its basin of attraction. However, we also demonstrate that the basins of attraction associated with a structurally stable - globally stable (robust) - planar system defined on a compact set are computable. Our findings suggest that the global stability of a system and the compactness of the domain play a pivotal role in determining the computability of its basins of attraction. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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