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

Jose-Luis Lopez·Ricardo Lopez-Ruiz
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Abstract

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

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Jose-Luis Lopez, Ricardo Lopez-Ruiz. 2002-05-14. The Limit Cycles of Lienard Equations in the Strongly Non-Linear Regime. https://arxiv.org/abs/nlin/0205027

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