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1.
A criterion of spatial chaos occurring in lattice dynamical systems—heteroclinic cycle—is discussed It is proved that if the
system has asymptotically stable heteroclinic cycle, then it has asymptotically stable homoclinic point which implies spatial
chaos.
Project supported by the National Natural Science Foundation of China. 相似文献
2.
In this paper, the heteroclinic bifurcation problem with real eigenvalues and two inclination-flips is investigated in a four-dimensional
reversible system. We perform a detailed study of this case by using the method originally established in the papers “Problems
in Homoclinic Bifurcation with Higher Dimensions” and “Bifurcation of Heteroclinic Loops,” and obtain fruitful results, such
as the existence and coexistence of R-symmetric homoclinic orbit and R-symmetric heteroclinic loops, R-symmetric homoclinic orbit and R-symmetric periodic orbit. The double R-symmetric homoclinic bifurcation (i.e., two-fold R-symmetric homoclinic bifurcation) for reversible heteroclinic loops is found, and the existence of infinitely many R-symmetric periodic orbits accumulating onto a homoclinic orbit is demonstrated. The relevant bifurcation surfaces and the
existence regions are also located.
This work was supported by National Natural Science Foundation of China (Grant No. 10671069) 相似文献
3.
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
4.
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
5.
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
6.
The existence of a rich structure of homoclinic and heteroclinic solutions is established for a family of Hamiltonian systems that serve as a simpler model for the multiple pendulum system. The proof is based on recently developed arguments from the calculus of variations that have proved useful in finding actual solutions of an equation near approximate solution.This research was sponsorted in part by the National Science Foundation under grant #MCS-8110556 and the U. S. Army Research Office under Contract #DAAL03-87-K-0043. Any reproduction for the purpose of the United States Government is permitted. 相似文献
7.
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
8.
Zhu Deming 《数学学报(英文版)》1996,12(4):372-378
Using the theory of invariant manifolds, we give local expressions of the stable and unstable manifolds for normally hyperbolic invariant tori, and study the existence of transverse orbits heteroclinic to hyperbolic invariant tori. These extend and improve the corresponding results obtained in [3–5].Supported by the National Natural Science Foundation of China and Shanghai Natural Science Foundation. 相似文献
9.
Ji-bin Li 《中国科学A辑(英文版)》2007,50(2):153-164
Using the methods of dynamical systems for the (n + 1)-dimensional multiple sine-Gordon equation, the existences of uncountably infinite many periodic wave solutions and breaking
bounded wave solutions are obtained. For the double sine-Gordon equation, the exact explicit parametric representations of
the bounded traveling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are
determined.
This work was supported by the National Natural Science Foundation of China (Grant No. 11671179) and the Natural Science Foundation
of Yunnan Province (Grant No. 2005A0092M). 相似文献
10.
New conditions for a planar homoclinic loop to have cyclicity two under multiple parameter perturbations have been obtained.
As an application it is proved that a homoclinic loop of a nongeneric cubic Hamiltonian has cyclicity two under arbitrary
quadratic perturbations.
Project supported by the National Natural Science Foundation of China (Grant Nos. 19531070 and 19771037). 相似文献
11.
Maoan Han 《中国科学A辑(英文版)》1997,40(12):1247-1258
A general method for a homoclinic loop of planar Hamiltonian systems to bifurcate two or three limit cycles under perturbations
is established. Certain conditions are given under which the cyclicity of a homoclinic loop equals 1 or 2. As an application
to quadratic systems, it is proved that the cyclicity of homoclinic loops of quadratic integrable and non-Hamiltonian systems
equals 2 except for one case.
Project supported by the National Natural Science Foundation of China. 相似文献
12.
Xiu-xiang Liu Pei-xuan Weng 《应用数学学报(英文版)》2006,22(3):369-386
We deal with asymptotic speed of wave propagation for a discrete reactlon-diffusion equation. We find the minimal wave speed c★ from the characteristic equation and show that c★ is just the asymptotic speed of wave propagation. The isotropic property and the existence of solution of the initial value problem for the given equation are also discussed. 相似文献
13.
By constructing a special cone and using cone compression and expansion fixed point theorem, this paper presents some existence
results of positive solutions of singular boundary value problem on unbounded domains for a class of first order differential
equation. As applications of the main results, two examples are given at the end of this paper.
Supported by the National Natural Science Foundation of China (No. 10671167) and the Natural Science Foundation of Liaocheng
University (31805). 相似文献
14.
Using the mixed monotone method we establish existence and uniqueness results for a singular integral equation. The theorem
obtained is very general and complements previous known results.
The work was supported by the National Natural Science Foundation of China (No.10571021 and No.10701020) and Key Laboratory
for Applied Statistics of MOE(KLAS) and Subject Foundation of Harbin University (No. HXK200714). 相似文献
15.
WANG YuShun WANG Bin & QIN MengZhao School of Mathematics Computer Science Nanjing Normal University Nanjing China LASG 《中国科学A辑(英文版)》2008,51(11):2115-2136
In this paper, we discuss the concept of local structure-preserving algorithms (SPAs) for partial differential equations,
which are the natural generalization of the corresponding global SPAs. Local SPAs for the problems with proper boundary conditions
are global SPAs, but the inverse is not necessarily valid. The concept of the local SPAs can explain the difference between
different SPAs and provide a basic theory for analyzing and constructing high performance SPAs. Furthermore, it enlarges the
applicable scopes of SPAs. We also discuss the application and the construction of local SPAs and derive several new SPAs
for the nonlinear Klein-Gordon equation.
This work was supported by the National Basic Research Program (Grant No. 2005CB321703). The first author was supported by
the National Natural Science Foundation of China (Grant Nos. 40405019, 10471067) and the Major Research Projects of Jiangsu
Province (Grant No. BK2006725); the second author was supported by the National Natural Science Foundation of China (Innovation
Group) (Grant No. 40221503) and the third author was supported by the National Natural Science Foundation of China (Grant
No. 10471145) 相似文献
16.
Tian Ze Wang 《数学学报(英文版)》2009,25(2):299-320
A necessary and sufficient solvable condition for diagonal quadratic equation with prime variables in arithmetic progressions is given, and the best qualitative bound for small solutions of the equation is obtained, 相似文献
17.
Feng Beiye 《应用数学学报(英文版)》1998,14(4):404-413
This paper gives a sufficient condition for the existence of heteroclinic cycle in the model of competition betweenn species and a criterion for determining the stability of the heteroclinic cycle. The results given in this paper extend the
results obtained by May and Leonard in and by Hofbauer and Sigmund in. A conjecture on the permanence of the model and a open
problem on the stability of the heteroclinic cycle for the critical case are given at the end of this paper.
This research is supported by the National Natural Science Foundation of China 相似文献
18.
By using Krasnoselskii‘s fixed-point theorem on a suitable cone, several existence results and corresponding properties of positive solutions of nonlocal boundary value problem for nonlinear retarded differential equation are obtained. 相似文献
19.
In this note, we apply numerical analysis to the first equation, find the conditions for it to have oscillating solutions and therefore solve an open problem posed by Peter A. Clarkson. 相似文献
20.
Hongwei LOU 《数学年刊B辑(英文版)》2008,29(5):521-530
The author proves that the on the singular set of a local solution to existence of an optimal control problem. right-hand term of a p-Laplace equation is zero the equation. Such a result is used to study the 相似文献