Bifurcation Analysis of a Multi-Parameter Liénard Polynomial System

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.