共查询到17条相似文献,搜索用时 78 毫秒
1.
Codimension 3 nonresonant bifurcations of homoclinic orbits with two inclination flips 总被引:5,自引:0,他引:5
SHUI Shuliang & ZHU Deming College of Mathematics Physics Zhejiang Normal University Jinhua China Department of Mathematics East China Normal University Shanghai China 《中国科学A辑(英文版)》2005,48(2):248-260
Homoclinic bifurcations in four-dimensional vector fields are investigated by setting up a local coordinate near a homoclinic orbit. This homoclinic orbit is principal but its stable and unstable foliations take inclination flip. The existence, nonexistence, and uniqueness of the 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the two-fold 1 -periodic orbit and three-fold 1 -periodic orbit are also obtained. It is indicated that the number of periodic orbits bifurcated from this kind of homoclinic orbits depends heavily on the strength of the inclination flip. 相似文献
2.
The paper studies a codimension-4 resonant homoclinic bifurcation with one orbit flip and two inclination flips, where the resonance takes place in the tangent direction of homoclinic orbit.Local active coordinate system is introduced to construct the Poincar′e returning map, and also the associated successor functions. We prove the existence of the saddle-node bifurcation, the perioddoubling bifurcation and the homoclinic-doubling bifurcation, and also locate the corresponding 1-periodic orbit, 1-homoclinic orbit, double periodic orbits and some 2n-homoclinic orbits. 相似文献
3.
Heteroclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near a rough heteroclinic loop. This heteroclinic loop has a principal heteroclinic orbit and a non-principal heteroclinic orbit that takes orbit flip. The existence, nonexistence, coexistence and uniqueness of the 1-heteroclinic loop, 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the two-fold or three-fold 1-periodic orbit is also obtained. 相似文献
4.
In this paper, the authors develop new global perturbation techniques for detecting the persistence of transversal homoclinic orbits in a more general nondegenerated system with action-angle variable. The unperturbed system is assumed to have saddle-center type equilibrium whose stable and unstable manifolds intersect in one dimensional manifold, and does not have to be completely integrable or near-integrable. By constructing local coordinate systems near the unperturbed homoclinic orbit, the conditions of existence of transversal homoclinic orbit are obtained, and the existence of periodic orbits bifurcated from homoclinic orbit is also considered. 相似文献
5.
《Annals of Differential Equations》2008,(1):52-64
The homoclinic bifurcations under resonant conditions are considered in the ho- moclinic manifold consisting of a series of homoclinic orbits for the fourth-dimensional system.The existence,coexistence and uniqueness of 1-homoclinic orbit,1-periodic orbit and 2-fold 1-periodic orbit are obtained under resonant condition,the correspon- ding bifurcation surfaces and existing regions are also given. 相似文献
6.
XU Yan-cong GENG Feng-jie 《高校应用数学学报(英文版)》2014,29(1):108-118
In this paper, the complicated dynamics is studied near a double homoclinic loops with bellows configuration for general systems. For the non-twisted multiple homoclinics, the existence of periodic orbit with the specified route and the existence of shift-invariant curve sequences defined on the cross sections of multiple homoclinics corresponding to any specified one-side infinite sequences are given. In addition, the existence regions are also located. 相似文献
7.
Analyses of Bifurcations and Stability in a Predator-prey System with Holling Type-Ⅳ Functional Response 总被引:9,自引:0,他引:9
Ji-caiHuang Dong-meiXiao 《应用数学学报(英文版)》2004,20(1):167-178
In this paper the dynamical behaviors of a predator-prey system with Holling Type-Ⅳfunctionalresponse are investigated in detail by using the analyses of qualitative method,bifurcation theory,and numericalsimulation.The qualitative analyses and numerical simulation for the model indicate that it has a unique stablelimit cycle.The bifurcation analyses of the system exhibit static and dynamical bifurcations including saddle-node bifurcation,Hopf bifurcation,homoclinic bifurcation and bifurcation of cusp-type with codimension two(ie,the Bogdanov-Takens bifurcation),and we show the existence of codimension three degenerated equilibriumand the existence of homoclinic orbit by using numerical simulation. 相似文献
8.
Qianqian Ji Weipeng Zhang Qiuying Lu Xiaodong Li 《Journal of Nonlinear Modeling and Analysis》2020,2(1):25-44
In this work, bifurcation analysis near double homoclinic loops with Ws inclination ?ip of Γ1 and nonresonant eigenvalues is presented in a four-dimensional system. We establish a Poincar´e map by constructing local active coordinates approach in some tubular neighborhood of unperturbed double homoclinic loops. Through studying the bifurcation equations, we obtain the condition that the original double homoclinic loops are persistent, and get the existence or the nonexistence regions of the large 1-homoclinic orbit and the large 1-periodic orbit. At last, an analytical example is given to illustrate our main results. 相似文献
9.
同宿及异宿轨线的研究近况 总被引:1,自引:0,他引:1
The bifurcation near a homoclinc orbit or a heteroclinic orbit has been interesting thenathematicians in recent years. This paper surveys the recent advance in the research onthis topic from four aspects; I. the existence of the homoclinic orbits and the heteroclinc。rbits; II. the stability of a homoclinc cycle or a heteroclinic cycle; III. the mutual positionbetween the stable manifold and the unstable manifold of a saddle point; IV。 the bifur-cation of a homoclinc orbit or a heteroclinic orbit. We especially survey some important results obtained by Russian and Chinese mathematicians. Some research dircections and problems are suggested for further study. 相似文献
10.
The authors study the bifurcation of homoclinic orbits from a degenerate homoclinic orbit in reversible system. The unperturbed system is assumed to have saddle-center type equilibrium whose stable and unstable manifolds intersect in two-dimensional manifolds. A perturbation technique for the detection of symmetric and nonsymmetric homoctinic orbits near the primary homoclinic orbits is developed. Some known results are extended. 相似文献
11.
A high-codimension homoclinic bifurcation is considered with one orbit flip and two inclination flips accompanied by resonant principal eigenvalues. A local active coordinate system in a small neighborhood of homoclinic orbit is introduced. By analysis of the bifurcation equation, the authors obtain the conditions when the original flip homoclinic orbit is kept or broken. The existence and the existence regions of several double periodic orbits and one triple periodic orbit bifurcations are proved. Moreover, the complicated homoclinic-doubling bifurcations are found and expressed approximately. 相似文献
12.
本文研究4 维系统中一类具有轨道翻转和倾斜翻转的退化异维环分支问题. 通过在未扰异维环的小管状邻域内建立局部活动坐标系, 本文建立Poincaré 映射, 确定分支方程. 由对分支方程的分析,本文讨论在小扰动下, 异宿环、同宿环和周期轨的存在性、不存在性和共存性, 且给出它们的分支曲面以及共存区域, 推广了已有结果. 相似文献
13.
This article is devoted to investigating the bifurcations of a heterodimensional cycle with orbit flip and inclination flip, which is a highly degenerate singular cycle. We show the persistence of the heterodimensional cycle and the existence of bifurcation surfaces for the homoclinic orbits or periodic orbits. It is worthy to mention that some new features produced by the degeneracies that the coexistence of heterodimensional cycles and multiple periodic orbits are presented as well, which is different from some known results in the literature. Moreover, an example is given to illustrate our results and clear up some doubts about the existence of the system which has a heterodimensional cycle with both orbit flip and inclination flip. Our strategy is based on moving frame, the fundamental solution matrix of linear variational system is chose to be an active local coordinate system along original heterodimensional cycle, which can clearly display the non-generic properties-``orbit flip" and ``inclination flip" for some sufficiently large time. 相似文献
14.
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
15.
Xingbo LIU 《数学年刊B辑(英文版)》2011,32(6):905-916
The bifurcations of orbit flip homoclinic loop with nonhyperbolic equilibria are investigated. By constructing local coordinate
systems near the unperturbed homoclinic orbit, Poincaré maps for the new system are established. Then the existence of homoclinic
orbit and the periodic orbit is studied for the system accompanied with transcritical bifurcation. 相似文献
16.
Tian Si ZHANG De Ming ZHU 《数学学报(英文版)》2006,22(3):855-864
Codimension-3 bifurcations of an orbit-flip homoclinic orbit with resonant principal eigenvalues are studied for a four-dimensional system. The existence, number, co-existence and noncoexistence of 1-homoclinic orbit, 1-periodic orbit, 2n-homoclinic orbit and 2n-periodic orbit are obtained. The bifurcation surfaces and existence regions are also given. 相似文献
17.
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