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.
متن کاملMedium Amplitude Limit Cycles of Some Classes of Generalized Liénard Systems
The bifurcation of limit cycles by perturbing a planar system which has a continuous family of cycles, i.e. periodic orbits, has been an intensively studied phenomenon; see for instance [13, 16, 2] and references therein. The simplest planar system having a continuous family of cycles is the linear center, and a special family of its perturbations is given by the generalized polynomial Liénard ...
متن کاملThe Cyclicity of Period Annuli of Some Classes of Reversible Quadratic Systems
The cyclicity of period annuli of some classes of reversible and non-Hamiltonian quadratic systems under quadratic perturbations are studied. The argument principle method and the centroid curve method are combined to prove that the related Abelian integral has at most two zeros.
متن کاملMaximum amplitude of limit cycles in Liénard systems.
We establish sufficient criteria for the existence of a limit cycle in the Liénard system x[over ̇]=y-ɛF(x),y[over ̇]=-x, where F(x) is odd. In their simplest form the criteria lead to the result that, for all finite nonzero ɛ, the amplitude of the limit cycle is less than ρ and 0≤a≤ρ≤u, where F(a)=0 and ∫(0)(u)F(x)dx=0. We take the van der Pol oscillator as a specific example and establish that ...
متن کاملLimit Cycles in Two Types of Symmetric LiÉnard Systems
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: Communications on Pure and Applied Analysis
سال: 2015
ISSN: 1534-0392
DOI: 10.3934/cpaa.2015.14.2127