共查询到20条相似文献,搜索用时 359 毫秒
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Philip J. Aston Alastair Spence Wu Wei 《Journal of Computational and Applied Mathematics》1997,80(2):277-297
The nonlinear equation f(x,λ,) = 0, f:X × R2→X, where X is a Banach space and f satisfies a Z2-symmetry relation is considered. Interest centres on a certain type of double singular point, where the solution x is symmetric and fx has a double zero eigenvalue, with one eigenvector symmetric and one antisymmetric.
We show that under certain nondegeneracy conditions, which are stated both algebraically and geometrically, there exists a path of Hopf bifurcations or imaginary Hopf bifurcations passing through the double singular point, and for which x is not symmetric except at the double singular point. An easy geometrical test is found to decide which type of phenomenon occurs. A biproduct of the analysis is that explicit expressions are obtained for quantities which help to provide a reliable numerical method to compute these paths. A pseudo-spectral method was used to obtain numerical results for the Brusselator equations to illustrate the theory. 相似文献
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王贺元 《高等学校计算数学学报(英文版)》2001,10(2)
1 IntroductionConsider the parameter dependent equationu"+ (λ+ s(μ) ) f( u) -μsinx =0 in ( 0 ,π)u( 0 ) =u(π) =0 ( 1 .1 )whereλ,μ∈R are parameters and f:R→R and S:R→R are smooth odd functions anda) f′( 0 ) =1 , b) f ( 0 )≠ 0 , c) s( 0 ) =0 , d) s′( 0 ) =1 . ( 1 .2 )Let S:u( x)→ u(π-x) ,Γ ={ S,I} ,then ( 1 .1 ) isΓ -equivariant.The equality ( 1 .2 a) isjust a normalization of f at x=0 .Otherwise,one may reseek the parameter x to ensure( 1 .2 a) .To simplify an… 相似文献
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Using bifurcation techniques, we investigate the existence of multiple solutions for a class of fourth order semipositone m-point boundary value problems. Our results improve those in the literature. 相似文献
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Using the cone theory and lattice structure, we discuss the existence of asymptotic bifurcation points and the global bifurcation of nonlinear operators which are not assumed to be cone mappings and may not be Frechet differentiable at points at infinity. As an application, the structure of the set of solutions of the superlinear Sturm-Liouville problems is investigated. 相似文献
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A two-dimensional discrete system of a species in two patches proposed by Newman et al. is studied. It is shown that the unique interior steady state is globally asymptotically stable if the active population has a Beverton–Holt type growth rate. If the population is also subject to Allee effects, then the system has two interior steady states whenever the density-independent growth rate is large. In addition, the model has period-two solutions if the symmetric dispersal exceeds a critical threshold. For small dispersal, populations may either go extinct or eventually stabilize. However, populations are oscillating over time if dispersal is beyond the critical value and the initial populations are large. 相似文献
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In this paper we investigate the homoclinic bifurcation properties near an eight-figure homoclinic orbit of co-dimension two of a planar dynamical system. The corresponding local bifurcation diagram is also illustrated by numerical computation. 相似文献
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迭代微分方程解的存在性及分支 总被引:5,自引:0,他引:5
本文讨论迭代微分方程x(t)=f(x(t),x(x(t)))的解的性态,并在f(x(t),x(x(t)))=(x^2(t)-μ)x(x(t))时研究解的分支问题,更正了现有文献中的错误,结出了正确,完整的结果。 相似文献
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In this paper, an interesting and new bifurcation phenomenon that limit cycles could be bifurcated from nilpotent node (focus) by changing its stability is investigated. It is different from lowing its multiplicity in order to get limit cycles. We prove that $n^2+n-1$ limit cycles could be bifurcated by this way for $2n+1$ degree systems. Moreover, this upper bound could be reached. At last, we give two examples to show that $N(3)=1$ and $N(5)=5$ respectively. Here, $N(n)$ denotes the number of small-amplitude limit cycles around a nilpotent node (focus) with $n$ being the degree of polynomials in the vector field. 相似文献
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讨论多参数非线性方程F(λ,x)=0的分歧问题,给出了(λ0,0)是F(λ,x)=0的分歧点的一个充分条件. 相似文献
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Lana Horvat Dmitrović 《Journal of Difference Equations and Applications》2013,19(7):1033-1054
In this article we show how a change of a box dimension of orbits of two-dimensional discrete dynamical systems is connected to their bifurcations in a non-hyperbolic fixed point. This connection is already shown in the case of one-dimensional discrete dynamical systems and Hopf bifurcation for continuous systems. Namely, at the bifurcation point the box dimension changes from zero to a certain positive value which is connected to the appropriate bifurcation. We study a two-dimensional discrete dynamical system with only one multiplier on the unit circle, and show a result for the box dimension of an orbit on the centre manifold. We also consider a planar discrete system undergoing a Neimark–Sacker bifurcation. It is shown that box dimension depends on the order of non-degeneracy at the non-hyperbolic fixed point and on the angle–displacement map. As it was expected, we prove that the box dimension is different in the rational and irrational case. 相似文献
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本文提出了采用摄动格式求解非线性方程组的解曲线跟踪算法的计算格式.文中着重讨论了解曲线上非正则点的搜索,以及从这些非正则点——转向点或分枝点——继续跟踪超临界平衡路径的计算方法.文中把这一算法应用于弹性薄壳的屈曲分析。通过柱壳和环壳的算例得到它们的整个屈曲过程的平衡路径和变形形态. 相似文献
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In this paper,the bifurcation problem g(x, λ) = 0 with symmetry con-dition is studied. An extended system is introduced for computing the simple high order symmetry-breaking bifurcation point. Numerical example is given. Key words Bifurcation problem, Symmetry-breaking bifurcation point, High order Singularities 相似文献
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We study the dynamical properties about fixed points, the existence of prime period and periodic points, and transcritical bifurcation of a one-dimensional laser model in . For the special case, we explore the global dynamics about fixed points, boundedness of positive solution, construction of invariant rectangle, existence of prime period-2 solution, construction of forbidden set, the existence of a prime period and periodic points, and transcritical bifurcation of the discrete-time laser model. Finally, theoretical results are illustrated using numerical simulations. 相似文献
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Joachim Haase Gerd Pönisch 《Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences》2013,19(2):107-121
An approach to determine turning points in electromechanical systems is presented and applied to the determination of pull-in parameters. The pull-in phenomenon is an inherent instability in devices using electrostatic actuation where an electrostatic force works against an elastic restoring force. The paper presents a relation between multi-valued characteristics describing MEMS devices and weakly singular tracking problems. The technique of augmented systems that characterize turning points is applied to the analytical and numerical determination of pull-in parameters. The method is discussed using a computer algebra system and a VHDL-AMS simulation engine. 相似文献
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Bai-sheng Wu 《计算数学(英文版)》1998,(5)
1.IntroductionThispaperisdevotedtothecalculatiollofT,ranchesofHopfpointswhichemallatefromacertaillsingularPointofatwopar:lmeterII()nlinearsystemwhereXisarealHillersspac(},Aabifllrcationparallleter,oranadditionalcontrolparameter,alldgisasnlootllmapping.\Nreassllllle(HI)gisA--synlnletric:thereexistsalillearoperators:X-Xsatisfying(I:identicaloperatorillX)Itiswellknottrnthat(1.2)irldllcestilesplittillgl)Th.firstauthorhasbeedsupportedbyar(>searchgralltoftileV'Olkswagen-StiftungWesaythatxiss… 相似文献