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 共查询到20条相似文献,搜索用时 9 毫秒
1.
一类可逆三次系统的等时中心   总被引:1,自引:0,他引:1  
对于一般多项式系统,给出可逆代数条件推导算法;对于一类可逆三次系统,提出周期系数改进算法,得到原点为等时中心的充要条件.  相似文献   

2.
In this paper we discuss bifurcation of critical periods in an m-th degree time-reversible system, which is a perturbation of an n-th degree homogeneous vector field with a rigidly isochronous center at the origin. We present period-bifurcation functions as integrals of analytic functions which depend on perturbation coefficients and reduce the problem of critical periods to finding zeros of a judging function. This procedure gives not only the number of critical periods bifurcating from the period annulus but also the location of these critical periods. Applying our procedure to the case n=m=2 we determine the maximum number of critical periods and their location; to the case n=m=3 we investigate the bifurcation of critical periods up to the first order in ε and obtain the expression of the second period-bifurcation function when the first one vanishes.  相似文献   

3.
论广义Liénard系统的全局中心   总被引:2,自引:0,他引:2  
刘朝杰  邵先喜  许成 《数学学报》2003,46(1):29-034
本文讨论了广义Liénard系统的局部和全局中心,给出了两个定理,它们推广和改进了文[1—3]的结果.文中引理对研究广义Liénard系统解的震荡性,稳定性和极限环的存在性也是有用的.  相似文献   

4.
哈密顿函数H(x,y)=F(x)+G(y)所对应的哈密顿系统.给出了这类系统的周期解的周期为单调函数的几个充分条件,并用所得结果讨论了Volterral-Lotka系统和无阻尼、无强迫Duffing方程周期解周期的单调性.  相似文献   

5.
This paper gives a theorem for the local center of generalized Lienard system; the relative theorems in the references can be deduced from our corollaries.  相似文献   

6.
This paper discusses the local and global center of the generalized Lienard system, gives two theorems which extend and improve the relative results of [1]-[3]. Moreover the lemmas in this paper are also useful to the study for the oscillation, stability and the existence of limit cycles of the generalized Lienard system.  相似文献   

7.
We extend the classical Belitskii normal form theorem uniformly for planar nilpotent foci and limit cycles. Then by using fractal analysis, isochronous properties near such invariant sets are well investigated.  相似文献   

8.
We study polynomial systems with degeneracy at infinity and a center-focus equilibrium at the origin. We give some general properties related to the existence of polynomial commutators and use these properties in order to characterize uniformly isochronous polynomial centers with polynomial commutator and, also, we show that the commutator of the centers of the analytic systems whose angular speed is constant can be chosen of radial form. Finally, we characterize the systems (−y+Ps+∑j=kn−1xHj,x+Qs+∑j=kn−1yHj)t with polynomial commutator, with Pj,Qj,Hj and Kj homogeneous polynomials.  相似文献   

9.
关于系统(x)=h(y)-F(x),(y)=-g(x) 的中心   总被引:4,自引:0,他引:4  
本文给出了广义Lienard系统的原点为局部中心和全局中心的几个充分条件及原点为全局中心的充要条件,所得结果推广和改进了文献[1-6]的结果.  相似文献   

10.
与几何凹函数相关的函数的准线性研究   总被引:2,自引:0,他引:2  
先介绍四个与几何凹函数定积分有关的不等式,后相应定义了四个函数,证明了它们具有某种准线性.作为应用,由此可得到这些函数的单调性,使得这四个不等式在理论上得到推广和完善,并且部分解决了一个公开问题.  相似文献   

11.
In this paper we present the necessary and sufficient conditions for linearizability of the planar time-reversible cubic complex system , . From these conditions, the necessary and sufficient conditions for the origin to be an isochronous center of the time-reversible cubic real system , can be obtained. Thus, the isochronous center problem of time-reversible cubic systems is solved completely.  相似文献   

12.
Motivated by a classical pendulum clock model suggested by Andrade in 1920, we study the equation and prove that for a nonlinear analytic the origin is never an isochronous focus or an isochronous center.

  相似文献   


13.
针对函数F(x)=x∫0(x-ct)f(t)dt的单调性,通过反例说明某文献的相关论述存在错误,并给出命题,全面讨论此类函数在各种情况下的单调性.  相似文献   

14.
ZHU Huan-ran 《数学季刊》2004,19(2):164-171
By using exponential dichotomies and Liapunov function method, we have studied the existence of almost periodic solutions on a Lienard system and have obtained some simple sufficient condition.  相似文献   

15.
We prove the absolute monotonicity or complete monotonicity of some determinant functions whose entries involve
modified Bessel functions Iν, Kν, the confluent hypergeometric function Φ, and the Tricomi function Ψ. Our results recover and generalize some known determinantal inequalities. We also show that a certain determinant formed by the Fibonacci numbers are nonnegative while determinants involving Hermite polynomials of imaginary arguments are shown to be completely monotonic functions.  相似文献   

16.
研究一类五次系统无穷远点的中心、拟等时中心条件与极限环分支问题.首先通过同胚变换将系统无穷远点转化成原点,然后求出该原点的前8个奇点量,从而导出无穷远点成为中心和最高阶细焦点的条件,在此基础上给出了五次多项式系统在无穷远点分支出8个极限环的实例.同时通过一种最新算法求出无穷远点为中心时的周期常数,得到了拟等时中心的必要条件,并利用一些有效途径一一证明了条件的充分性.  相似文献   

17.
In this paper, the authors are concerned with the forced isochronous oscillators with a repulsive singularity and a bounded nonlinearity $$ x' + V'(x) + g(x) = e(t,x,x'), $$ where the assumptions on $V$, $g$ and $e$ are regular, described precisely in the introduction. Using a variant of Moser's twist theorem of invariant curves, the authors show the existence of quasi-periodic solutions and boundedness of all solutions. This extends the result of Liu to the case of the above system where $e$ depends on the velocity.  相似文献   

18.
In this paper we study the linearizability problem of polynomial-like complex differential systems. We give a reduction of linearizability problem of such non-polynomial systems to the problem of polynomial systems. Applying this reduction, we find some linearizability conditions for a time-reversible quartic-like complex system and derive from them conditions of isochronous center for the corresponding real system.  相似文献   

19.
There are many methods such as Gröbner basis, characteristic set and resultant, in computing an algebraic set of a system of multivariate polynomials. The common difficulties come from the complexity of computation, singularity of the corresponding matrices and some unnecessary factors in successive computation. In this paper, we decompose algebraic sets, stratum by stratum, into a union of constructible sets with Sylvester resultants, so as to simplify the procedure of elimination. Applying this decomposition to systems of multivariate polynomials resulted from period constants of reversible cubic differential systems which possess a quadratic isochronous center, we determine the order of weak centers and discuss the bifurcation of critical periods.  相似文献   

20.
利用Picard-Fuchs方程,研究了一类二次可逆系统周期函数的单调性问题,获得了在首次积分曲线是亏格1时的二次可逆系统周期函数单调的结论.  相似文献   

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