Graça, DanielZhong, Ning2026-05-112026-05-112024-06-261860-5974http://hdl.handle.net/10400.1/28921In this paper, we examine the relationship between the stability of the dynamical system x ′ = f(x) and the computability of its basins of attraction. We present a computable C ∞ system x ′ = 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.engNon-computabilityBasin of attractionDynamical systemsOrdinary differential equationsStructural stabilityjournal article10.46298/lmcs-20(2:19)2024