Dynamical analysis of a cubic Liénard system with global parameters. II. (Q2813865)

The authors examine the global dynamics of the cubic Liénard system NEWLINE\[NEWLINE\dot x = y, \dot y = a + b x + c y - x^3 - x^2 y,\quad a,b,c \in {\mathbb R}NEWLINE\]NEWLINE in the case of three equilibria. After determining the topological type of the equilibria and investigating the existence of limit cycles and homoclinic loops, they derive the bifurcation diagram and all possible phase portraits. Using these results they are able to provide a positive answer to an earlier conjecture regarding the surface of double limit cycles, as well as determination of a parameter region for the nonexistence of figure-eight loops.