On Lienard oscillator models with a pregiven set of limit cycles
نویسندگان
چکیده
منابع مشابه
Uniqueness of limit cycles for a class of Lienard systems
39 We shall give three ' criteria for the uniqueness of limit cycles of systems of Liellard type x '= a(y)-f3(y)F(x}, y '= -g(x}, examples are provided to illustrate our results.
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We divide R2 in l sectors S1, ..., Sl, with l > 1 even. We define in R2 a discontinuous differential system such that in each sector Sk, for k = 1, ..., l, is defined a smooth generalized Lienard polynomial differential equation ẍ + fi(x)ẋ + gi(x) = 0, i = 1, 2 alternatively, where fi and gi are polynomials of degree n−1 and m respectively. We apply the averaging theory of first order for disco...
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Liénard equations, ẍ+ ǫf(x)ẋ+ x = 0, with f(x) an even continuous function are considered. In the weakly nonlinear regime (ǫ → 0), the number and a O(ǫ0) approximation of the amplitude of limit cycles present in this type of systems, can be obtained by applying a methodology recently proposed by the authors [López-Ruiz R, López JL. Bifurcation curves of limit cycles in some Liénard systems. Int...
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Liénard equations of the form ẍ + ǫf(x)ẋ + x = 0, with f(x) an even function, are considered in the weakly nonlinear regime (ǫ → 0). A perturbative algorithm for obtaining the number, amplitude and shape of the limit cycles of these systems is given. The validity of this algorithm is shown and several examples illustrating its application are given. In particular, an O(ǫ8) approximation for the...
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ژورنال
عنوان ژورنال: Mathematical Modelling
سال: 1986
ISSN: 0270-0255
DOI: 10.1016/0270-0255(86)90058-8