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@article{561508,
author = {Baráková, Lenka},
article_location = {Tbilisi},
article_number = {2},
keywords = {Hopf bifurcation; limit cycle; invariant set},
language = {eng},
issn = {1072-947X},
journal = {Georgian Mathematical Journal},
title = {Asymptotic behaviour and Hopf bifurcation of a three-dimensional nonlinear autonomous system},
volume = {9},
year = {2002}
}
TY - JOUR
ID - 561508
AU - Baráková, Lenka
PY - 2002
TI - Asymptotic behaviour and Hopf bifurcation of a three-dimensional nonlinear autonomous system
JF - Georgian Mathematical Journal
VL - 9
IS - 2
SP - 207-226
EP - 207-226
PB - Heldermann Verlag
SN - 1072947X
KW - Hopf bifurcation
KW - limit cycle
KW - invariant set
N2 - A three-dimensional real nonlinear autonomous system of a concrete type is studied. The Hopf bifurcation is analysed and the existence of a limit cycle is proved. A positively invariant set, which is globally attractive, is found using a a suitable Lyapunov-like function.Corollaries for a cubic system are presented. Also, a two-dimensional nonlinear system is studied as a restricted system. An application in economic to the Kodera's model of inflation is presented.
ER -
BARÁKOVÁ, Lenka. Asymptotic behaviour and Hopf bifurcation of a three-dimensional nonlinear autonomous system. \textit{Georgian Mathematical Journal}. Tbilisi: Heldermann Verlag, 2002, roč.~9, č.~2, s.~207-226. ISSN~1072-947X.
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