Limit cycles for rigid cubic systems
نویسندگان
چکیده
منابع مشابه
Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems
We study the maximum number of limit cycles that bifurcate from the periodic solutions of the family of isochronous cubic polynomial centers ẋ = y(−1+2αx+2βx), ẏ = x+α(y−x)+ 2βxy, α ∈ R, β < 0, when it is perturbed inside the classes of all continuous and discontinuous cubic polynomial differential systems. We obtain that the maximum number of limit cycles which can be obtained by the averaging...
متن کاملLimit Cycles for Cubic Systems with a Symmetry of Order 4 and without Infinite Critical Points
In this paper we study those cubic systems which are invariant under a rotation of 2π/4 radians. They are written as ż = εz + p z2z̄ − z̄3, where z is complex, the time is real, and ε = ε1+ iε2, p = p1+ ip2 are complex parameters. When they have some critical points at infinity, i.e. |p2| ≤ 1, it is well-known that they can have at most one (hyperbolic) limit cycle which surrounds the origin. On ...
متن کاملExact Number of Limit Cycles for a Family of Rigid Systems
For a given family of planar differential equations it is a very difficult problem to determine an upper bound for the number of its limit cycles. Even when this upper bound is one it is not always an easy problem to distinguish between the case of zero and one limit cycle. This note mainly deals with this second problem for a family of systems with a homogeneous nonlinear part. While the condi...
متن کاملExistence Conditions of Thirteen Limit Cycles in a cubic System
As we know, the second part of the Hilbert problem is to find the maximal number and relative locations of limit cycles of polynomial systems of degree n. Let H(n) denote this number, which is called the Hilbert number. Then the problem of finding H(n) is divided into two parts: find an upper and lower bounds of it. For the upper bound there are important works of Écalle [1990] and IIyashenko a...
متن کاملLimit cycles of cubic polynomial differential systems with rational first integrals of degree 2
The main goal of this paper is to study the maximum number of limit cycles that bifurcate from the period annulus of the cubic centers that have a rational first integral of degree 2 when they are perturbed inside the class of all cubic polynomial differential systems using the averaging theory. The computations of this work have been made with Mathematica and Maple.
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: 2005
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2004.07.030