Small-amplitude limit cycles of certain Liénard systems

Source abstract

Abstract The paper is concerned with the number of limit cycles of systems of the form ẋ = y–F(x), ẏ = –g(x), where F and g are polynomials. For several classes of such systems, the maximum number of limit cycles that can bifurcate out of a critical point under perturbation of the coefficients in F and g is obtained (in terms of the degree of F and g).