The paper deals with the characterization of Hopf bifurcations in families of simple nonlinear systems, i.e., third-order autonomous systems with few nonlinear terms. By employing Harmonic Balance (HB) tools, the complete set of system parameters corresponding to supercritical and subcritical bifurcations is determined. In addition, it is shown how parameters defining supercritical bifurcations can be used as starting points in bifurcation analysis, in order to locate quite simple system able to display complex behaviours.
Hopf bifurcation analysis for simple third-order quadratic systems / Innocenti, Giacomo; Genesio, Roberto; Tesi, Alberto. - STAMPA. - Analysis and Control of Chaotic Systems, Volume 1, Part 1:(2006), pp. 227-232. (Intervento presentato al convegno 1st IFAC Conference on Analysis and Control of Chaotic Systems tenutosi a Reims, France nel 2006/06/28-30) [10.3182/20060628-3-FR-3903.00041].
Hopf bifurcation analysis for simple third-order quadratic systems
INNOCENTI, GIACOMO;GENESIO, ROBERTO;TESI, ALBERTO
2006
Abstract
The paper deals with the characterization of Hopf bifurcations in families of simple nonlinear systems, i.e., third-order autonomous systems with few nonlinear terms. By employing Harmonic Balance (HB) tools, the complete set of system parameters corresponding to supercritical and subcritical bifurcations is determined. In addition, it is shown how parameters defining supercritical bifurcations can be used as starting points in bifurcation analysis, in order to locate quite simple system able to display complex behaviours.
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