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@article{561505,
author = {Baráková, Lenka},
article_number = {3},
keywords = {Limit cycle; invariant set; Hopf bifurcation},
language = {eng},
issn = {0420-1213},
journal = {Demonstratio Mathematica},
title = {Asymptotic behaviour and existence of a limit cycle of cubic autonomous systems},
volume = {34},
year = {2001}
}
TY - JOUR
ID - 561505
AU - Baráková, Lenka
PY - 2001
TI - Asymptotic behaviour and existence of a limit cycle of cubic autonomous systems
JF - Demonstratio Mathematica
VL - 34
IS - 3
SP - 560-576
EP - 560-576
SN - 04201213
KW - Limit cycle
KW - invariant set
KW - Hopf bifurcation
N2 - 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.
ER -
BARÁKOVÁ, Lenka. Asymptotic behaviour and existence of a limit cycle of cubic autonomous systems. \textit{Demonstratio Mathematica}. 2001, roč.~34, č.~3, s.~560-576, 18 s. ISSN~0420-1213.
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