共查询到18条相似文献,搜索用时 62 毫秒
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韩茂安 《高校应用数学学报(A辑)》1999,14(4):421-426
在具余维2奇点的四维系统的两参数开折的研究中出现一类三点异宿环的扰动分支,对此异宿环产生极限环的唯一性一直未得到完整的解决,本文圆满地解决了这一问题,并获得了全局分支中极限环的唯一性。 相似文献
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一类两点异宿环的扰动分支 总被引:1,自引:0,他引:1
设Lo为含两个双曲鞍点Si(i=1,2)的异宿环,Si的双曲比记为Tio(i=1,2),Mourtada在1994年证明如果未扰动系统与被扰系统均为C∞的,则当r10r20≠1时,Lo至多产生两个极限环.本文对C3系统证明了这一结论. 相似文献
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设 L0为含两个双曲鞍点 Si(i= 1,2)的异宿环, Si的双曲比记为ri0(i= 1,2), Mourtada在1994年证明如果未扰动系统与被扰系统均为 C∞的,则当r10,20≠1时, L0至多产生两个极限环.本文对 C3系统证明了这一结论. 相似文献
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对余维3系统Xμ(x)具有包含一个双曲鞍-焦点O1和一个非双曲鞍-焦点O2的异宿环£进行了研究.证明了在£的邻域内有可数无穷条周期轨线和异宿轨线,当非粗糙异宿轨线ΓO破裂时Xμ(x)会产生同宿轨分支,并给出了相应的分支曲线和两种同宿环共存的参数值.在3参数扰动下ΓO破裂和O2点产生Hopf分支的情况下,在£的邻域内有一条含O1点同宿环,可数无数多条的轨线同宿于O2点分支出的闭轨HO,一条或无穷多条(可数或连续统的)异宿轨线等. 相似文献
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DENG Guifeng ZHU Deming 《数学年刊A辑(中文版)》2007,(5)
对余维3系统X_μ(x)具有包含一个双曲鞍-焦点O_1和一个非双曲鞍-焦点O_2的异宿环f进行了研究.证明了在f的邻域内有可数无穷条周期轨线和异宿轨线,当非粗糙异宿轨线Γ~0破裂时X_μ(x)会产生同宿轨分支,并给出了相应的分支曲线和两种同宿环共存的参数值.在3参数扰动下Γ~0破裂和O_2点产生Hopf分支的情况下,在f的邻域内有一条含O_1点同宿环,可数无效多条的轨线同宿于O_2点分支出的闭轨H_0,一条或无穷多条(可数或连续统的)异宿轨线等. 相似文献
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一类三次Kolmogorov系统的极限环分支 总被引:1,自引:0,他引:1
本文研究了一类三次Kolmogorov系统,得出了该系统可分支出三个极限环,且其中有两个是稳定的,同时给出了其中心条件. 相似文献
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Han Maoan 《数学年刊B辑(英文版)》1998,19(2):189-196
§1.NormalFormsofDisplacementFunctionsConsideraplanarC∞systemoftheformx=f(x)+λf0(x,δ,λ)≡f(x,δ,λ),(1.1)wherex∈R2,λ∈R,δ∈Rm,andtr... 相似文献
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Xianbo SunMaoan Han Junmin Yang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(9):2948-2965
In this article, we study the expansion of the first Melnikov function of a near-Hamiltonian system near a heteroclinic loop with a cusp and a saddle or two cusps, obtaining formulas to compute the first coefficients of the expansion. Then we use the results to study the problem of limit cycle bifurcation for two polynomial systems. 相似文献
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In this paper, the authors consider limit cycle bifurcations for a kind of nonsmooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with a center at the origin and a heteroclinic loop around the origin. When the degree of perturbing polynomial terms is n(n ≥ 1), it is obtained that n limit cycles can appear near the origin and the heteroclinic loop respectively by using the first Melnikov function of piecewise near-Hamiltonian systems, and that there are at most n + [(n+1)/2] limit cycles bifurcating from the periodic annulus between the center and the heteroclinic loop up to the first order in ε. Especially, for n = 1, 2, 3 and 4, a precise result on the maximal number of zeros of the first Melnikov function is derived. 相似文献
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Sun Jianhua 《数学年刊B辑(英文版)》1994,15(4):493-500
THEUNIQUENESSOFBIFURCATIONTOSEPARATRIXLOOPSINSUPERCRITICALCASES¥SUNJIANHUA(DepartmentofMathematics,NanjingUniversity,Nanjing2... 相似文献
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This paper concerns with the bifurcation of limit cycles from a double homoclinic loop under multiple parameter perturbations for general planar systems. The existence conditions of 4 homoclinic bifurcation curves and small and large limit cycles are especially investigated. 相似文献
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In this paper, we deal with the problem of limit cycle bifurcation near a 2-polycycle or 3-polycycle for a class of integrable systems by using the first order Melnikov function. We first get the formal expansion of the Melnikov function corresponding to the heteroclinic loop and then give some computational formulas for the first coefficients of the expansion. Based on the coefficients, we obtain a lower bound for the maximal number of limit cycles near the polycycle. As an application of our main results, we consider quadratic integrable polynomial systems, obtaining at least two limit cycles. 相似文献
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This paper deals with Liénard equations of the form , , with P and Q polynomials of degree 5 and 4 respectively. Attention goes to perturbations of the Hamiltonian vector fields with an elliptic Hamiltonian of degree six, exhibiting a double figure eight loop. The number of limit cycles and their distributions are given by using the methods of bifurcation theory and qualitative analysis. 相似文献
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Han Maoan 《数学学报(英文版)》1997,13(1):64-75
The author first investigates the limit cycles bifurcating from a center for general two dimensional systems, and then proves
the conjecture that any unfolding of the cusp of ordern has at mostn−1 limit cycles.
Supported by the Chinese National Natural Science Foundation. 相似文献