Bifurcation Analysis of a Multi-Parameter Liénard Polynomial System
V. Gaiko (National Academy of Sciences of Belarus)
C. Vuik (TU Delft - Numerical Analysis)
Huibert A.J. Reijm (Student TU Delft)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
In this paper, we study a multi-parameter Liénard polynomial system carrying out its global bifurcation analysis. To control the global bifurcations of limit cycle in this systems, it is necessary to know the properties and combine the effects of all its field rotation parameters. It can be done by means of the development of our bifurcational geometric method based on the application of a canonical system with field rotation parameters. Using this method, we present a solution of Hilbert's Sixteenth Problem on the maximum number of limit cycles and their distribution for the Liénard polynomial system. We also conduct some numerical experiments to illustrate the obtained results.