In this note we investigate the problem of computing the domain of attraction of a flow on ℝ2 for a given attractor. We consider an operator that takes two inputs, the description of the flow and a cover of the attractors, and outputs the domain of attraction for the given attractor. We show that: (i) if we consider only (structurally) stable systems, the operator is (strictly semi-)computable; (ii) if we allow all systems defined by C 1-functions, the operator is not (semi-)computable. We also address the problem of computing limit cycles on these systems. © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Graça, D. S., & Zhong, N. (2009). Computing domains of attraction for planar dynamics. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5715 LNCS, pp. 179–190). https://doi.org/10.1007/978-3-642-03745-0_22
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