caa a22 4500 445842865 CHVBK 20180317145350.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s11047-010-9230-0 doi (NATIONALLICENCE)springer-10.1007/s11047-010-9230-0 Computability in planar dynamical systems [Elektronische Daten] [Daniel Graça, Ning Zhong] In this paper we explore the problem of computing attractors and their respective basins of attraction for continuous-time planar dynamical systems. We consider C 1 systems and show that stability is in general necessary (but may not be sufficient) to attain computability. In particular, we show that (a) the problem of determining the number of attractors in a given compact set is in general undecidable, even for analytic systems and (b) the attractors are semi-computable for stable systems. We also show that the basins of attraction are semi-computable if and only if the system is stable. Springer Science+Business Media B.V., 2010 Computability nationallicence Planar dynamical systems nationallicence Equilibrium points nationallicence Limit cycles nationallicence Basins of attraction nationallicence Graça Daniel DM/FCT, Universidade do Algarve, C. Gambelas, 8005-139, Faro, Portugal aut Zhong Ning DMS, University of Cincinnati, 45221-0025, Cincinnati, OH, USA aut Natural Computing Springer Netherlands 10/4(2011-12-01), 1295-1312 1567-7818 10:4<1295 2011 10 11047 https://doi.org/10.1007/s11047-010-9230-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11047-010-9230-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Graça Daniel DM/FCT, Universidade do Algarve, C. Gambelas, 8005-139, Faro, Portugal aut NATIONALLICENCE 700 1- Zhong Ning DMS, University of Cincinnati, 45221-0025, Cincinnati, OH, USA aut NATIONALLICENCE 773 0- Natural Computing Springer Netherlands 10/4(2011-12-01), 1295-1312 1567-7818 10:4<1295 2011 10 11047 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer