共查询到20条相似文献,搜索用时 31 毫秒
1.
研究了一类3维反转系统中包含2个鞍点的对称异维环分支问题, 且仅限于研究系统的线性对合R的不变集维数为1的情形.
给出了R-对称异宿环与R-对称周期轨线存在和共存的条件, 同时也得到了R-对称的重周期轨线存在性. 其
次, 给出了异宿环、 同宿轨线、 重同宿轨线和单参数族周期轨线的存在性、 唯一性和共存性等结论,
并且发现不可数无穷条周期轨线聚集在某一同宿轨线的小邻域内. 最后给出了相应的分支图. 相似文献
2.
De Ming ZHU Ying SUN 《数学学报(英文版)》2007,23(8):1495-1504
In this paper, we study the dynamical behavior for a 4-dimensional reversible system near its heteroclinic loop connecting a saddle-focus and a saddle. The existence of infinitely many reversible 1-homoclinic orbits to the saddle and 2-homoclinic orbits to the saddle-focus is shown. And it is also proved that, corresponding to each 1-homoclinic (resp. 2-homoclinic) orbit F, there is a spiral segment such that the associated orbits starting from the segment are all reversible 1-periodic (resp. 2-periodic) and accumulate onto F. Moreover, each 2-homoclinic orbit may be also accumulated by a sequence of reversible 4-homoclinic orbits. 相似文献
3.
By using the linear independent fundamental solutions of the linear variational equation
along the heteroclinic loop to establish a suitable local coordinate system in some small tubular neighborhood
of the heteroclinic loop, the Poincaré map is constructed to study the bifurcation problems of
a fine 3–point loop in higher dimensional space. Under some transversal conditions and the non–twisted
condition, the existence, coexistence and incoexistence of 2–point–loop, 1–homoclinic orbit, simple 1–periodic orbit and 2–fold
1–periodic orbit, and the number of 1–periodic orbits are studied. Moreover,
the bifurcation surfaces and existence regions are given. Lastly, the above bifurcation results are applied
to a planar system and an inside stability criterion is obtained.
This work is supported by the National Natural Science Foundation of China (10371040), the Shanghai Priority
Academic Disciplines and the Scientific Research Foundation of Linyi Teacher’s University 相似文献
4.
John Franks 《Publications Mathématiques de L'IHéS》1990,71(1):105-120
Letf be an orientation preserving diffeomorphism ofR
2 which preserves area. We prove the existence of infinitely many periodic points with distinct rotation numbers around a fixed
point off, provided only thatf has two fixed points whose infinitesimal rotation numbers are not both 0.
We also show that if a fixed pointz off is enclosed in a “simple heteroclinic cycle” and has a non-zero infinitesimal rotation numberr, then for every non-zero rational numberp/q in an interval with endpoints 0 andr, there is a periodic orbit inside the heteroclinic cycle with rotation numberp/q aroundz. 相似文献
5.
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
6.
Bifurcations of heterodimensional cycles with two saddle points 总被引:1,自引:0,他引:1
The bifurcations of 2-point heterodimensional cycles are investigated in this paper. Under some generic conditions, we establish the existence of one homoclinic loop, one periodic orbit, two periodic orbits, one 2-fold periodic orbit, and the coexistence of one periodic orbit and heteroclinic loop. Some bifurcation patterns different to the case of non-heterodimensional heteroclinic cycles are revealed. 相似文献
7.
Bifurcations of heterodimensional cycles with highly degenerate conditions are studied by establishing a suitable local coordinate system in three-dimensional vector fields. The existence, coexistence and noncoexistence of the periodic orbit, homoclinic loop, heteroclinic loop and double periodic orbit are obtained under some generic hypotheses. The bifurcation surfaces and the existence regions are located; the number of the bifurcation surfaces exhibits variety and complexity of the bifurcation of degenerate heterodimensional cycles. The corresponding bifurcation graph is also drawn. 相似文献
8.
Bifurcations of a degenerate homoclinic orbit with orbit flip in high dimensional system are studied. By establishing a local
coordinate system and a Poincaré map near the homoclinic orbit, the existence and uniqueness of 1–homoclinic orbit and 1–periodic
orbit are given. Also considered is the existence of 2–homoclinic orbit and 2–periodic orbit. In additon, the corresponding
bifurcation surfaces are given.
Project supported by the National Natural Science Foundation of China (No: 10171044), the Natural Science Foundation of Jiangsu
Province (No: BK2001024), the Foundation for University Key Teachers of the Ministry of Education of China 相似文献
9.
In this paper, we study the weak type heterodimensional cycle with orbit-flip in its non-transversal orbit by using the local moving frame approach. For the first two subcases, we present the sufficient conditions for the existence, uniqueness and non-coexistence of the homoclinic orbit, heteroclinic orbit and periodic orbit. Based on the bifurcation analysis, the bifurcation surfaces and the existence regions are located. And for the third subcase, we theoretically established both the coexistence conditio... 相似文献
10.
11.
LOCALIZED PATTERNS OF THE CUBIC-QUINTIC SWIFT-HOHENBERG EQUATIONS WITH TWO SYMMETRY-BREAKING TERMS 下载免费PDF全文
Homoclinic snake always refers to the branches of homoclinic orbits \mbox{near} a heteroclinic cycle connecting a hyperbolic or non-hyperbolic equilibrium and a periodic
orbit in a reversible variational system. In this paper, the normal form of a Swift-Hohenberg equation with two different symmetry-breaking terms (non-reversible term and non-k-symmetry term) are investigated by using multiple scale method, and their bifurcation diagrams are initially studied by numerical simulations. Typically, we predict numerically the existence of so-called round-snakes and round-isolas upon particular two symmetric-breaking perturbations. 相似文献
12.
Bifurcations of nontwisted and fine heteroclinic loops are studied for higher dimensional systems. The existence and its associated
existing regions are given for the 1-hom orbit and the 1-per orbit, respectively, and bifurcation surfaces of the two-fold
periodic orbit are also obtained. At last, these bifurcation results are applied to the fine heteroclinic loop for the planar
system, which leads to some new and interesting results. 相似文献
13.
Bifurcations of heteroclinic loops 总被引:14,自引:0,他引:14
By generalizing the Floquet method from periodic systems to systems with exponential dichotomy, a local coordinate system
is established in a neighborhood of the heteroclinic loop Γ to study the bifurcation problems of homoclinic and periodic orbits.
Asymptotic expressions of the bifurcation surfaces and their relative positions are given. The results obtained in literature
concerned with the 1-hom bifurcation surfaces are improved and extended to the nontransversal case. Existence regions of the
1-per orbits bifurcated from Γ are described, and the uniqueness and incoexistence of the 1-hom and 1-per orbit and the inexistence
of the 2-hom and 2-per orbit are also obtained.
Project supported by the National Natural Science Foundation of China (Grant No. 19771037) and the National Science Foundation
of America # 9357622. This paper was completed when the first author was visiting Northwestern University. 相似文献
14.
For the system of Lorenz equations in the parameter space we construct a complete bifurcation diagram of all homoclinic and
heteroclinic separatrix contours of singular points that exist in the system. These constructs include the existence surface
of a homoclinic butterfly, the existence half-surface of homoclinic loops of saddle-focus separatrices, and the existence
curve of a heteroclinic separatrix contour joining a saddle-node with two saddle-foci. 相似文献
15.
金银来 《高校应用数学学报(英文版)》2003,18(2):186-192
§ 1 HypothesesConsider the following system:z.=f(z) , (1 .1 )and its perturbed systemz.=f(z) +g(z,μ) (1 .2 )where z∈ Rm+n,μ∈ Rk,k≥ 3,0≤ |μ| 1 ,f,g∈ Cr,r≥ 4 ,g(z,0 ) =0 .For simplicity,we sup-pose thatf(p) =0 ,g(p,μ) =0 .Moreover,for(1 .1 ) we assume(H1 ) The stable manifold Wspand the unstable manifold Wupof z=p are m-dimension-al and n-dimensional,respectively.The linearization Df(p) atthe equilibrium z=p has realmultiple-2 eigenvaluesλ1 and -ρ1 ,such thatany remaining eige… 相似文献
16.
We study the R-controllability (the controllability within the attainability set) and the R-observability of time-varying linear differential-algebraic equations (DAE). We analyze DAE under assumptions guaranteeing
the existence of a structural form (which is called “equivalent”) with separated “differential” and “algebraic” subsystems.
We prove that the existence of this form guarantees the solvability of the corresponding conjugate system, and construct the
corresponding “equivalent form” for the conjugate DAE. We obtain conditions for the R-controllability and R-observability, in particular, in terms of controllability and observability matrices. We prove theorems that establish certain
connections between these properties. 相似文献
17.
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
18.
Jens D.M. Rademacher 《Journal of Differential Equations》2005,218(2):390-443
We analyze homoclinic orbits near codimension-1 and -2 heteroclinic cycles between an equilibrium and a periodic orbit for ordinary differential equations in three or higher dimensions. The main motivation for this study is a self-organized periodic replication process of travelling pulses which has been observed in reaction-diffusion equations. We establish conditions for existence and uniqueness of countably infinite families of curve segments of 1-homoclinic orbits which accumulate at codimension-1 or -2 heteroclinic cycles. The main result shows the bifurcation of a number of curves of 1-homoclinic orbits from such codimension-2 heteroclinic cycles which depends on a winding number of the transverse set of heteroclinic points. In addition, a leading order expansion of the associated curves in parameter space is derived. Its coefficients are periodic with one frequency from the imaginary part of the leading stable Floquet exponents of the periodic orbit and one from the winding number. 相似文献
19.
20.
Clodoaldo Grotta Ragazzo 《纯数学与应用数学通讯》1997,50(2):105-147
We consider 4-dimensional, real, analytic Hamiltonian systems with a saddle center equilibrium (related to a pair of real and a pair of imaginary eigenvalues) and a homoclinic orbit to it. We find conditions for the existence of transversal homoclinic orbits to periodic orbits of long period in every energy level sufficiently close to the energy level of the saddle center equilibrium. We also consider one-parameter families of reversible, 4-dimensional Hamiltonian systems. We prove that the set of parameter values where the system has homoclinic orbits to a saddle center equilibrium has no isolated points. We also present similar results for systems with heteroclinic orbits to saddle center equilibria. © 1997 John Wiley & Sons, Inc. 相似文献