The limit cycles of Liénard equations in the strongly nonlinear regime

Liénard systems of the form , with f(x) an even function, are studied in the strongly nonlinear regime ( →∞). A method for obtaining the number, amplitude and loci of the limit cycles of these equations is derived. The accuracy of this method is checked in several examples. Lins–Melo–Pugh conjecture for the polynomial case is true in this regime.