Asymptotic behaviour and Hopf bifurcation of a three-dimensional nonlinear autonomous system
| Authors | |
|---|---|
| Year of publication | 2002 |
| Type | Article in Periodical |
| Magazine / Source | Georgian Mathematical Journal |
| MU Faculty or unit | |
| 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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