Limit Cycles of a Class of Generalized Liénard Polynomial Equations
نویسنده
چکیده
In this paper we study the maximum number of limit cycles of the following generalized Liénard polynomial differential system of the first order ẋ = y2p−1 ẏ = −x2q−1 − εf (x, y) where p and q are positive integers, ε is a small parameter and f (x, y) is a polynomial of degree m. We prove that this maximum number depends on p, q and m. AMS subject classification:
منابع مشابه
Limit Cycles of the Generalized Polynomial Liénard Differential Equations
We apply the averaging theory of first, second and third order to the class of generalized polynomial Liénard differential equations. Our main result shows that for any n, m ≥ 1 there are differential equations of the form ẍ+f(x)ẋ+g(x) = 0, with f and g polynomials of degree n and m respectively, having at least [(n + m− 1)/2] limit cycles, where [·] denotes the integer part function.
متن کاملBifurcations of Multiple Relaxation Oscillations in Polynomial Liénard Equations
In this paper, we prove the presence of limit cycles of given multiplicity, together with a complete unfolding, in families of (singularly perturbed) polynomial Liénard equations. The obtained limit cycles are relaxation oscillations. Both classical Liénard equations and generalized Liénard equations are treated.
متن کاملRelationships between Darboux Integrability and Limit Cycles for a Class of Able Equations
We consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmPxyPxyPxy++++2(,)(,)(,)nnmnmyQxyQxyQxy++&=++. For where and are homogeneous polynomials of degree i. Inside this class of polynomial differential equation we consider a subclass of Darboux integrable systems. Moreover, under additional conditions we proved such Darboux integrable systems can have at most 1 limit cycle.
متن کاملThe number of medium amplitude limit cycles of some generalized Liénard systems
We will consider two special families of polynomial perturbations of the linear center. For the resulting perturbed systems, which are generalized Liénard systems, we provide the exact upper bound for the number of limit cycles that bifurcate from the periodic orbits of the linear center.
متن کاملMaximum Number and Distribution of Limit Cycles in the General Liénard Polynomial System
In this paper, using our bifurcational geometric approach, we complete the solution of the problem on the maximum number and distribution of limit cycles in the general Liénard polynomial system. AMS Subject Classifications: 34C05, 34C07, 34C23, 37G05, 37G10, 37G15.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016