Global dynamics of a non-symmetric cubic Lienard system

Abstract:

In this paper, we study global dynamics of a cubic non-symmetric Lienard system with global parameters, i.e., parameters are not required to be sufficiently small. After analyzing qualitative properties of all the equilibria and discussing the existence of limit cycles and heteroclinic orbits, we give a complete classification of the global phase portraits in the Poincare disc. Finally, associated with the previous results we obtain the bifurcation diagram in the parameter space.