Phase portraits of the quadratic polynomial Liénard differential systems

Abstract

We classify the global phase portraits in the Poincaré disc of the quadratic polynomial Liénard differential systems \dot{x}=y, \quad \dot{y}=(ax+b)y+cx^2+dx+e, where (x, y) ∈ ℝ2 are the variables and a,b,c,d,e are real parameters.