Limit Periodic Sets in Polynomial Liénard Equations
نویسندگان
چکیده
منابع مشابه
On 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 کاملDifferential Equations with Limit-periodic Forcings
The present paper is concerned with scalar differential equations of first order which are limit periodic in the independent variable. Some tools provided by the theories of exponential dichotomies and periodic differential equations are applied to prove that, in a generic sense, the existence of a bounded solution implies the existence of a limit periodic solution.
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 کامل2 The Limit Cycles of Liénard Equations in the Strongly Nonlinear Regime
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.
متن کاملRegression for sets of polynomial equations
We propose a method called ideal regression for approximating an arbitrary system of polynomial equations by a system of a particular type. Using techniques from approximate computational algebraic geometry, we show how we can solve ideal regression directly without resorting to numerical optimization. Ideal regression is useful whenever the solution to a learning problem can be described by a ...
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: Qualitative Theory of Dynamical Systems
سال: 2008
ISSN: 1575-5460,1662-3592
DOI: 10.1007/s12346-008-0019-9