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  • A 2-dimensional real autonomous system with polynomial right-hand side is studied. Hopf bifurcation is analysed and existence of a limit cycle is proved. A new formula to determine stability or instability of this limit cycle is introduced. A positively invariant set, which is globally attractive, is found. Existence of a stable limit cycle around an unstable critical point is proved. An application in economics to the dynamic version of the neo-keynesian macroeconomic IS-LM model is presented.
  • A 2-dimensional real autonomous system with polynomial right-hand side is studied. Hopf bifurcation is analysed and existence of a limit cycle is proved. A new formula to determine stability or instability of this limit cycle is introduced. A positively invariant set, which is globally attractive, is found. Existence of a stable limit cycle around an unstable critical point is proved. An application in economics to the dynamic version of the neo-keynesian macroeconomic IS-LM model is presented. (en)
  • V práci je studován reálný autonomní systém s polynomiální pravou stranou. Je analyzována Hopfova bifurkace a dokázána existence limitního cyklu. Je uveden nový vzorec pro určení stability nebo nestability tohoto limitního cyklu. Je nalezena globálně atrahující pozitivně invariantní množina a dokázána existence stabilního limitního cyklu kolem nestabilního kritického bodu. Je prezentována ekonomická aplikace na dynamickou verzi neo-keynesiánského makroekonomického IS-LM modelu. (cs)
Title
  • Asymptotické chování a existence limitního cyklu kubických autonomních systémů (cs)
  • Asymptotic behaviour and existence of a limit cycle of cubic autonomous systems
  • Asymptotic behaviour and existence of a limit cycle of cubic autonomous systems (en)
skos:prefLabel
  • Asymptotické chování a existence limitního cyklu kubických autonomních systémů (cs)
  • Asymptotic behaviour and existence of a limit cycle of cubic autonomous systems
  • Asymptotic behaviour and existence of a limit cycle of cubic autonomous systems (en)
skos:notation
  • RIV/00216224:14310/01:00021247!RIV08-MSM-14310___
http://linked.open.../vavai/riv/strany
  • 560-576
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  • 3
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  • 673976
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  • RIV/00216224:14310/01:00021247
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  • Limit cycle; invariant set; Hopf bifurcation (en)
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  • PL - Polská republika
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  • [BBA7CB5B0BF5]
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  • Demonstratio Mathematica
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  • 34
http://linked.open...iv/tvurceVysledku
  • Přibylová, Lenka
http://linked.open...n/vavai/riv/zamer
issn
  • 0420-1213
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  • 14310
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