Limit cycles of some polynomial Liénard systems
نویسندگان
چکیده
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 کاملOn 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...
متن کاملOn the Number of Limit Cycles for Discontinuous Generalized Liénard Polynomial Differential Systems
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...
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2012
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2011.11.070