The Limit Cycles of Lienard Equations in the Strongly Non-Linear Regime

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Lienard systems of the form x+εf(x)x+x=0, with f(x) an even function, are studied in the strongly nonlinear regime (ε→∞). 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.