Bifurcation Curves of Limit Cycles in some Lienard Systems

Abstract

Lienard systems of the form $\ddot{x}+\epsilon f(x)\dot{x}+x=0$, with f(x) an even continous function, are considered. The bifurcation curves of limit cycles are calculated exactly in the weak ($\epsilon\to 0$) and in the strongly ($\epsilon\to\infty$) nonlinear regime in some examples. The number of limit cycles does not increase when $\epsilon$ increases from zero to infinity in all the cases analyzed.