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

Abstract

Lienard systems of the form $\ddot{x}+\epsilon f(x)\dot{x}+x=0$, with f(x) an even function, are studied in the strongly nonlinear regime ($\epsilon \to \infty$). 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.

22 pages, 0 figures. Published in Chaos, Solitons and Fractals, vol. 11, 747-756 (2001)

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