Bifurcations of small limit cycles in Lienard systems with cubic restoring terms

In this paper, we study bifurcations of small-amplitude limit cycles of Lienard systems of the form (x) over dot = y - F(x), (y) over dot = -g(x), where g(x) is a cubic polynomial, and F(x) is a smooth or piecewise smooth polynomial of degree n. By using involutions, we obtain sharp upper bounds of the number of small-amplitude limit cycles produced around a singular point for some systems of this type. (C) 2019 Elsevier Inc. All rights reserved.