Computing Domains of Attraction for Planar Dynamics

  • Daniel S. Graça
  • Ning Zhong
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5715)


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.


Equilibrium Point Computing Domain Computable Function Planar Dynamics Lorenz Attractor 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Daniel S. Graça
    • 1
    • 2
  • Ning Zhong
    • 3
  1. 1.DM/FCT, Universidade do Algarve, C. GambelasFaroPortugal
  2. 2.SQIG/Instituto de TelecomunicaçõesLisbonPortugal
  3. 3.DMS, University of CincinnatiCincinnatiU.S.A.

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