2 The Limit Cycles of Liénard Equations in the Strongly Nonlinear Regime
نویسنده
چکیده
Liénard systems of the form ẍ+ ǫf(x)ẋ+x = 0, with f(x) an even function, are studied in the strongly nonlinear regime (ǫ → ∞). 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.
منابع مشابه
Bifurcation Curves of Limit cycles in some LiéNard Systems
Liénard systems of the form ẍ + ǫf(x)ẋ + x = 0, with f(x) an even continous function, are considered. The bifurcation curves of limit cycles are calculated exactly in the weak (ǫ → 0) and in the strongly (ǫ → ∞) nonlinear regime in some examples. The number of limit cycles does not increase when ǫ increases from zero to infinity in all the cases analyzed.
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