{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:22Z","timestamp":1753894402281,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>In this paper, we examine the relationship between the stability of the\ndynamical system $x^{\\prime}=f(x)$ and the computability of its basins of\nattraction. We present a computable $C^{\\infty}$ system $x^{\\prime}=f(x)$ that\npossesses a computable and stable equilibrium point, yet whose basin of\nattraction is robustly non-computable in a neighborhood of $f$ in the sense\nthat both the equilibrium point and the non-computability of its associated\nbasin of attraction persist when $f$ is slightly perturbed. This indicates that\nlocal stability near a stable equilibrium point alone is insufficient to\nguarantee the computability of its basin of attraction. However, we also\ndemonstrate that the basins of attraction associated with a structurally stable\n- globally stable (robust) - planar system defined on a compact set are\ncomputable. Our findings suggest that the global stability of a system and the\ncompactness of the domain play a pivotal role in determining the computability\nof its basins of attraction.<\/jats:p>","DOI":"10.46298\/lmcs-20(2:19)2024","type":"journal-article","created":{"date-parts":[[2024,6,26]],"date-time":"2024-06-26T13:25:21Z","timestamp":1719408321000},"source":"Crossref","is-referenced-by-count":0,"title":["Robust non-computability of dynamical systems and computability of robust dynamical systems"],"prefix":"10.46298","volume":"Volume 20, Issue 2","author":[{"given":"Daniel S.","family":"Gra\u00e7a","sequence":"first","affiliation":[]},{"given":"Ning","family":"Zhong","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2024,6,26]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/13831\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/13831\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,26]],"date-time":"2024-06-26T13:25:21Z","timestamp":1719408321000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/11381"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,26]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-20(2:19)2024","relation":{"has-preprint":[{"id-type":"arxiv","id":"2305.14448v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2305.14448v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2305.14448","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2305.14448","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2024,6,26]]},"article-number":"11381"}}