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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, vol.~34, No~3, p.~560-576, 18 pp. ISSN~0420-1213.
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