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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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