共查询到19条相似文献,搜索用时 46 毫秒
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本文考虑奇摄动问题的位于快变量空间中的奇异同宿轨道的保存和周期轨道分支问题文中关于奇异同宿轨道保存的结论推广了一些已知的结果,而周期轨道产生于奇异同宿轨道的分支则提供了一种新的分支类型 相似文献
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本文研究具有非双曲奇点的高维系统在小扰动下的同宿轨道分支问题,通过在未扰同宿轨道邻域建立局部坐标系,导出系统在新坐标系下的Poincare映射,对伴随超临界分支的通有同宿轨道的保存及分支出周期轨道的情况进行了讨论,推广和改进了一些文献的结果. 相似文献
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该文研究带有角变量的快变振荡系统的同宿轨道分支问题,通过建立完整的Poincaré映射,讨论其同宿轨道在小扰动下的保存性, 并进一步研究其分支出周期轨道的情况,推广和改进了一些文献的结果. 相似文献
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考虑伴随超临界分支的高维非退化系统在非通有假设下的同宿轨道分支问题,通过在未扰同宿轨道邻域建立活动坐标架,导出系统在新坐标系下的全局Poincare映射,对伴随超临界分支的非通有同宿轨道的保存及分支周期轨道的情况导出相应的分支方程和分支图. 相似文献
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该文研究了具有轨道翻转的双同宿环四维系统,在主特征值共振和沿轨道奇点处切方向共振下的两种分支.我们分别在系统奇点小邻域内利用规范型的解构造一个奇异映射,再在双同宿环的管状邻域内引起局部活动坐标架,利用系统线性变分方程的解定义了一个正则映射,通过复合两个映射而得到分支研究中一类重要的Poincaré映射,经过简单的计算最终得到后继函数的精确表达式.对分支方程细致地研究,我们给出了原双同宿环的保存性条件,并证明了“大” 1-同宿环分支曲面,2-重“大”1-周期轨分支曲面,“大”2-同宿环分支曲面的存在性、存在区域和近似表达式,及其分支出的“大”周期轨和“大”同宿轨的存在性区域和数量. 相似文献
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本文考虑弱吸引条件下的Sil'nikov现象,证明了相应的Poincare映射具有马蹄构造,并且,伴随着广义Hopf分支,将产生新的同宿轨道、异宿轨道以及更复杂的混沌现象. 相似文献
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讨论了具有暂时免疫传染病模型同宿轨道分支的存在性,利用Melnikov函数确定了系统双曲不动点的稳定和不稳定流形的相对位置,从而给出存在极限环的参数范围. 相似文献
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The homoclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near the homoclinic orbit. This homoclinic orbit is non-principal in the meanings that its positive semi-orbit takes orbit flip and its unstable foliation takes inclination flip. The existence, nonexistence, uniqueness and coexistence of the 1-homoclinic orbit and the 1-periodic orbit are studied. The existence of the twofold periodic orbit and three-fold periodic orbit are also obtained. 相似文献
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BIFURCATIONOFDEGENERATEHOMOCLINICORBITS¥ZengWeiyao(HunanLightindustryCollege,410007)Abstract:Themainpurposeofthispaperistoinv... 相似文献
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DEGENERATED HOMOCLINIC BIFURCATIONS WITH HIGHER DIMENSIONS 总被引:13,自引:0,他引:13
91.IntroductionandHypothesesInrecelltyears)withthedevelopmelltofnonlinearscienceandthedeepstudyof~icphenomena,anincreasinglylargenUInberofpapersared~edtothebifurcationProblemsofhomocliulcandheterocbocorbitsinhighdhansionalspace(see11--14]).Duetothedifficultyencountered,uofortunately,onlyafew(e.g.[1,13,14])areconcernedwiththeperiodicorbitsbifulcatedfromsingularloops.Papers[1,131discussedtheProblemofthehomoclinicloOPbifurcationinhighdimensionwithcodimension2,thatis,thesystemhasresonanteigenVa… 相似文献
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In this paper, we study the bifurcation problems of rough heteroclinic loops connecting three saddle points for a higher-dimensional
system. Under some transversal conditions and the nontwisted condition, the existence, uniqueness, and incoexistence of the
1-heteroclinic loop with three or two saddle points, 1-homoclinic orbit and 1-periodic orbit near Γ are obtained. Meanwhile,
the bifurcation surfaces and existence regions are also given. Moreover, the above bifurcation results are extended to the
case for heteroclinic loop with l saddle points.
Received January 4, 2001, Accepted July 3, 2001. 相似文献
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本文研究三维系统的一类非双曲周期轨道在小扰动下产生周期轨道的问题,并对一类较特殊的系统给出了判别周期轨道存在的具体条件。此外,还给出了具体的应用例子。 相似文献
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弱Silnikov现象中的全局分支问题 总被引:1,自引:0,他引:1
本文考虑在一条同宿于具一对纯虚特征值的鞍-焦点的轨道邻域内的分支问题,证明了在同宿分支值的邻域内,存在着可数无穷多个鞍结点分支值,倍周期分支值和2-脉冲同宿分支值,并且两相邻鞍结点分支值的比趋于常数1。 相似文献
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BIFURCATION OF PERIODIC ORBITS OF A THREE-DIMENSIONAL SYSTEM 总被引:1,自引:0,他引:1
§ 1 . IntroductionThere has been a general theory on bifurcation of periodic orbits for two or higher-dimensional systems, and the theory for two-dimensional systems is much richer than thatfor higher-dimensional systems (see [1–11]). We have a relative… 相似文献
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THE EXISTENCE OF HOMOCLINIC ORBITS FOR HAMILTONIAN
SYSTEMS WITH THE POTENTIALS CHANGING SIGN 总被引:1,自引:0,他引:1
Fei Guihua 《数学年刊B辑(英文版)》1996,17(4):403-410
§1.IntroductionandMainResults WeconsidertheHamiltoniansystems¨q-L(t)q V′(t,q)=0,(HS)where(t,q)∈R×RN,¨q=d2dt2q,V′(t,q)denotesthegradientofV(t,q)withrespecttoq,andthesymmetricmatrixL(t)isassumedtosatisfy:(L)L(t)∈C(R,RN2)andthereexistsλ>0suchthatL(t)x·xλ|x|2,(t,x)∈R×RN.Weassum… 相似文献
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Problems in homoclinic bifurcation with higher dimensions 总被引:11,自引:0,他引:11
Zhu Deming 《数学学报(英文版)》1998,14(3):341-352
In this paper, a suitable local coordinate system is constructed by using exponential dichotomies and generalizing the Floquet
method from periodic systems to nonperiodic systems. Then the Poincaré map is established to solve various problems in homoclinic
bifurcations with codimension one or two. Bifurcation diagrams and bifurcation curves are given.
Project 19771037, supported by NSFC 相似文献