Asymptotic behaviour and existence of a limit cycle of cubic autonomous systems

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Authors	BARÁKOVÁ Lenka
Year of publication	2001
Type	Article in Periodical
Magazine / Source	Demonstratio Mathematica
MU Faculty or unit	Faculty of Science
Citation
Field	General mathematics
Keywords	Limit cycle; invariant set; Hopf bifurcation
Description	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.
Related projects:	Functional-differential equations and mathematical-statistical models