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

摘要

Lienard systems of the form $\ddot{x}+\epsilon f(x)\dot{x}+x=0$, with f(x) aneven function, are studied in the strongly nonlinear regime($\epsilon\to\infty$). A method for obtaining the number, amplitude and loci ofthe limit cycles of these equations is derived. The accuracy of this method ischecked in several examples. Lins-Melo-Pugh conjecture for the polynomial caseis true in this regime.