Asymptotic behaviour and Hopf bifurcation of a three-dimensional nonlinear autonomous system

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Authors

BARÁKOVÁ Lenka

Year of publication 2002
Type Article in Periodical
Magazine / Source Georgian Mathematical Journal
MU Faculty or unit

Faculty of Science

Citation
Field General mathematics
Keywords Hopf bifurcation; limit cycle; invariant set
Description 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.
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