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1.
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
2.
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
3.
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
4.
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
5.
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
6.
Deming Zhu 《数学学报(英文版)》1995,11(3):267-277
Under a generic assumption, the existence and the uniqueness of the periodic orbit generating from a homoclinic bifurcation are shown, and the dimensions of its stable and unstable manifolds are given. In the case of a 3-dimensional system, our result revises the stability criterion given in [4,5].Supported by the National Natural Science Foundation of China. 相似文献
7.
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
8.
JianHuaSUN 《数学学报(英文版)》2005,21(1):65-80
In this paper we study the singularity at the origin with three-fold zero eigenvalue forsymmetric vector fields with nilpotent linear part and 3-jet C^∞-equivalent to y δ/δx zδ/δy ax^2yδ/δz with a≠0. We first obtain several subfamilies of the symmetric versal unfoldings of this singularityby using the normal form and blow-up methods under some conditions, and derive the local and global bifurcation behavior, then prove analytically the existence of the Sil‘nikov homoclinic bifurcation for some subfamilies of the symmetric versal unfoldings of this singularity, by using the generalized Mel‘nikov methods of a homoclinic orbit to a hyperbolic or non-hyperbolic equilibrium in a highdimensional space. 相似文献
9.
Positive Periodic Solutions of a Class of Non-autonomous Single Species Population Model with Delays and Feedback Control 总被引:2,自引:0,他引:2
Feng De CHEN Xiao Xin CHEN Jin De CAO An Ping CHEN 《数学学报(英文版)》2005,21(6):1319-1336
With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, several verifiable criteria are established for the global existence of positive periodic solutions of a class of non-autonomous single species population model with delays (both state-dependent delays and continuous delays) and feedback control. After that, by constructing a suitable Lyapunov functional, sufficient conditions which guarantee the existence of a unique globally asymptotic stable positive periodic solution of a kind of nonlinear feedback control ecosystem are obtained. Our results extend and improve the existing results, and have further applications in population dynamics. 相似文献
10.
Shi Rong LI Xiu Yun GUO 《数学学报(英文版)》2007,23(4):731-734
A subgroup H of a finite group G is called a TI-subgroup if H ∩ H^x = 1 or H for all x ∈ G. In this paper, a complete classification for finite p-groups, in which all abelian subgroups are TI-subgroups, is given. 相似文献
11.
In this paper, we consider a three dimensional Ginzburg–Landau type equation with a periodic initial value condition. A fully
discrete Galerkin–Fourier spectral approximation scheme is constructed, and then the dynamical properties of the discrete
system are analyzed. First, the existence and convergence of global attractors of the discrete system are proved by a priori
estimates and error estimates of the discrete solution, and the numerical stability and convergence of the discrete scheme
are proved. Furthermore, the long-time convergence and stability of the discrete scheme are proved.
*This work was supported by the National Natural Science Foundation of China (No.: 10432010 and 10571010) 相似文献
12.
By the variable transformation and generalized Hirota method, exact homoclinic and heteroclinic solutions for Davey-Stewartson II (DSII) equation are obtained. For perturbed DSII equation, the existence of a global attractor is proved. The persistence of homoclinic and heteroclinic flows is investigated, and the special homoclinic and heteroclinic structure in attractors is shown. 相似文献
13.
The Existence of Positive Almost Periodic Type Solutions for Some Nonlinear Delay Integral Equations
Bin XU Rong YUAN 《数学学报(英文版)》2005,21(6):1351-1360
This paper presents the conditions of existence of positive almost periodic type solutions for some nonlinear delay integral equations, by using a fixed point theorem in the mixed monotone operators (Ma, Y.: On a class of mixed monotone operators and a kind of two-point bounded value problem. Indian J. Math., 41(2), 211-220 (1999]]. Some known results are operators. 相似文献
14.
HOMOCLINICORBITSFORSECONDORDERHAMILTONIANSYSTEMWITHQUADRATICGROWTHWUSHAOPINGANDLIUJIAQUANAbstract:Someexistenceandmultiplicit... 相似文献
15.
Ming Chun XU 《数学学报(英文版)》2005,21(4):899-902
In this paper the following theorem is proved: Every group L3(q) for q = 3^(2m-1)(m≥2) is characterized by its set of element orders. 相似文献
16.
Xiao Shan Chen 《Numerische Mathematik》2007,107(1):79-86
The purpose of this paper is to study the perturbation of generalized eigenvalues. Two perturbation bounds of the diagonalizable
pairs are given. These results extend the corresponding ones given by Sun (Math Numer Sinica 4:23–29, 1982).
This work is supported by the Natural Science Foundation of Guangdong Province (No. 06025061) and by the National Natural
Science Foundations of China (No. 10671077 and 10626021). 相似文献
17.
A Characterization of Continuous Module Homomorphisms on Random Semi—Normed Modules and Its Applications 总被引:1,自引:0,他引:1
TieXinGUO 《数学学报(英文版)》2003,19(1):201-208
In this paper,a characterization of continuous module homomorphisms on random seminormed modules is first given;then the characterization is further used to show that the Hahn-Banach type of extension theorem is still true for continuous module homomorphisms on random semi-normed modules. 相似文献
18.
Due to its good potential for digital signal processing, discrete Gabor analysis has interested some mathematicians. This
paper addresses Gabor systems on discrete periodic sets, which can model signals to appear periodically but intermittently.
Complete Gabor systems and Gabor frames on discrete periodic sets are characterized; a sufficient and necessary condition
on what periodic sets admit complete Gabor systems is obtained; this condition is also proved to be sufficient and necessary
for the existence of sets E such that the Gabor systems generated by χ
E
are tight frames on these periodic sets; our proof is constructive, and all tight frames of the above form with a special
frame bound can be obtained by our method; periodic sets admitting Gabor Riesz bases are characterized; some examples are
also provided to illustrate the general theory.
This work was supported by National Natural Science Foundation of China (Grant No. 10671008), Beijing Natural Science Foundation
(Grant No. 1092001), PHR (IHLB) and the project sponsored by SRF for ROCS, SEM of China 相似文献
19.
Cai Di ZHAO Yong Sheng LI Sheng Fan ZHOU 《数学学报(英文版)》2007,23(11):2043-2060
This paper discusses the Cauchy problem of elliptic-elliptic-type Davey-Stewartson systems with zero-order dissipation on R^2. Making use of the Fourier spectral projector, together with a long time comparison between the solutions to the Davey-Stewartson systems and to an auxiliary problem, we prove that the global attractor in H^1 (R^2) for the addressed Davey-Stewartson systems is a compact subset of H^2(R^2), and thus reveal the asymptotic smoothing effect of the solutions for the systems. 相似文献
20.
On Eigenvalue Intervals and Eigenfunctions of Nonresonance Singular Dirichlet Boundary Value Problems 总被引:1,自引:0,他引:1
Zhao-cai HaoDepartment of Mathematics Qufu Normal University Qufu China 《应用数学学报(英文版)》2002,18(4):569-578
In this paper we shall consider the nonresonance Dirichlet boundary value problemwhere λ>0 is a parameter, p>0 is a constant. Intervals of A are determined to ensure the existence of a nonnegative solution of the boundary value problem. For λ=1, we shall also offer criteria for the existence of eigenfunctions. The main results include and improve on those of [2,4,6,8]. 相似文献