Limit cycles of Liénard polynomial systems type by averaging method
نویسندگان
چکیده
منابع مشابه
On the Number of Limit cycles for a Generalization of LiéNard Polynomial differential Systems
where g1(x) = εg11(x)+ε g12(x)+ε g13(x), g2(x) = εg21(x) + ε g22(x) + ε g23(x) and f(x) = εf1(x) + εf2(x) + ε f3(x) where g1i, g2i, f2i have degree k, m and n respectively for each i = 1, 2, 3, and ε is a small parameter. Note that when g1(x) = 0 we obtain the generalized Liénard polynomial differential systems. We provide an upper bound of the maximum number of limit cycles that the previous d...
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In this paper, we investigate the number of limit cycles for a class of discontinuous planar differential systems with multiple sectors separated by many rays originating from the origin. In each sector, it is a smooth generalized Liénard polynomial differential system x′ = −y + g1(x) + f1(x)y and y′ = x + g2(x) + f2(x)y, where fi(x) and gi(x) for i = 1, 2 are polynomials of variable x with any...
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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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Liénard systems and their generalized forms are classical and important models of nonlinear oscillators, and have been widely studied by mathematicians and scientists. The main problem considered is the maximal number of limit cycles that the system can have. In this paper, two types of symmetric polynomial Liénard systems are investigated and the maximal number of limit cycles bifurcating from...
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ژورنال
عنوان ژورنال: Moroccan Journal of Pure and Applied Analysis
سال: 2020
ISSN: 2351-8227
DOI: 10.2478/mjpaa-2020-0001