Publication details
Asymptotic behaviour and existence of a limit cycle of cubic autonomous systems
| Authors | |
|---|---|
| Year of publication | 2001 |
| Type | Article in Periodical |
| Magazine / Source | Demonstratio Mathematica |
| MU Faculty or unit | |
| 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: |