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

• Autorzy: Barakova L.
• Języki publikacji: EN

Abstrakty

EN

In this paper a 2-dimensional real autonomous system with polynomial right-hand sides of a concrete type is studied. Hopf bifurcation is analysed and existence of a limit cycle is proved. A new formula to determine stability or unstability of this limit cycle is introduced. A positively invariant set, which is globally attractive, is found. Consequently, existence of a stable limit cycle around an unstable critical point is proved and also a sufficient condition for non-existence of a closed trajectory in the phase space is given. Global characteristics of the system are studied. An application in economics to the dynamic version of the neo-keynesian macroeconomic IS-LM model is presented.

Słowa kluczowe

EN

limit cycle; invariant sets; Hopf bifurcation

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 3
• Strony: 559--576
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Barakova L.

• Department of Mathematics Masaryk University Janackovo nam 2a 692 95 Brno, Czech Republic

Bibliografia

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