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1.
本文研究一维带有同号截距的分段线性映射动力系统的边界碰撞分叉问题.根据截距的位置关系,将问题分成两类,并采用Leonov方法来研究边界碰撞分叉曲线.另外确定了边界碰撞分叉曲线和flip分叉曲线所围成的周期区域.研究结果表明,当分段线性映射具有同号截距时,其具有非常丰富的周期结构. 相似文献
2.
引进正则移位不变集的概念,证明了有正则移位不变集的紧致系统在几乎周期点集中存在SS混沌集,特别地,具有正拓扑熵的区间映射在几乎周期点集中存在SS混沌集. 相似文献
3.
几乎周期性与SS混沌集 总被引:6,自引:0,他引:6
引进正则移位不变集的概念,证明了有正则移位不变集的紧致系统在几乎周期点集中存在SS混沌集,特别地,具有正拓扑熵的区间映射在几乎周期点集中存在SS混沌集. 相似文献
4.
本文考虑一类超线性Hill型对称碰撞方程的对称碰撞周期解的存在性、重性和分布问题.通过坐标变换的方法把碰撞相平面转化为全平面进行研究,在一类关于时间映射的超线性条件下证明有外力方程无穷多个对称碰撞调和解和对称碰撞次调和解的存在性;同时研究在没有外力时方程的对称碰撞周期解的稠密性分布.本文还给出对称碰撞方程对称碰撞周期解存在的充分条件. 相似文献
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赵学志 《数学年刊A辑(中文版)》2003,(2)
相对Nielsen周期点理论是讨论形如f:(X,A)→(X,A)映射的周期点个数估计问题,本文对已知的估计量给予统一的处理.利用这种方法,定义了两个新的Nielsen型数, NPn(f;X-A)和NΦn(f;X-A),它们分别是映射f在cl(X-A)中的n周期点和最小周期为n的周期点个数的下界. 相似文献
8.
本文在Q-正则Loewner空间中用环模不等式刻划了拟对称映射.另外,在 Q-维Ahlfors-David正则空间中建立了拟对称映射作用下的Grotzsch-Teichmuller型 模不等式,它是通过伸张系数的积分平均来表示. 相似文献
9.
研究了具有双侧弹性约束的单自由度悬臂梁系统擦边诱导的非光滑动力学行为.首先,基于弹性碰撞悬臂梁的动力学方程和擦边点的定义,分析了双侧擦边周期运动的存在性条件.其次,选取零速度的Poincaré截面,推导了双侧擦边轨道附近带参数的高阶不连续映射.然后,结合光滑流映射和高阶不连续映射建立了新的复合分段范式映射.最后,将基于低阶范式映射和高阶范式映射得到的分岔图进行对比,分析验证了高阶范式映射的有效性,并通过数值仿真进一步揭示了弹性碰撞悬臂梁的擦边动力学. 相似文献
10.
考虑一类具有两个自由度的弱耦合对称碰撞方程的对称碰撞周期解的存在性、重性问题.在一类关于时间映射的超线性条件下证明了方程无穷多个对称碰撞调和解和对称碰撞次调和解的存在性.同时,还给出了一个适合两个自由度的对称碰撞方程的对称碰撞周期解存在的充分条件. 相似文献
11.
J. C. Valverde 《Acta Mathematica Hungarica》2000,88(1-2):113-121
One way to deal with bifurcations in the theory of dynamical systems is to find some normal forms of the system, that is, doing some changes of coordinates, the system can be led to a similar form to that given for the normal forms. But usually it is a complicated problem to elucidate if the truncated normal form of the system is (locally) topologically conjugated to the normal one. Here, we provide a way to avoid this problem when we study bifurcations, through the consideration of the surface of the fixed points which allows us to generalize the non-degenerated conditions of certain bifurcations to appear. 相似文献
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In this paper, we consider an implicit 2-variable first-order partial differential equation with complete integral. As an application of the Legendrian singularity theory, we give a generic classification of bifurcations of such differential equations with respect to the equivalence relation which is given by the group of point transformations following S. Lie?s view. Since two one-parameter unfoldings of such differential equations are equivalent if and only if induced one-parameter unfoldings of integral diagrams are equivalent for generic equations, our normal forms are represented by one-parameter integral diagrams. 相似文献
13.
Kazuyuki Yagasaki 《Journal of Differential Equations》2002,185(1):1-24
Using a Melnikov-type technique, we study codimension-two bifurcations called the Bogdanov-Takens bifurcations for subharmonics in periodic perturbations of planar Hamiltonian systems. We give a criterion for the occurrence of the Bogdanov-Takens bifurcations and present approximate expressions for saddle-node, Hopf and homoclinic bifurcation sets near the Bogdanov-Takens bifurcation points. We illustrate the theoretical result with an example. 相似文献
14.
Given a family of nonlinear control systems, where the Jacobian of the driver vector field at one equilibrium has a simple
zero eigenvalue, with no other eigenvalues on the imaginary axis, we split it into two parts, one of them being a generic
family, where it is possible to control the stationary bifurcations: saddle-node, transcritical and pitchfork bifurcations,
and the other one being a non-generic family, where it is possible to control the transcritical and pitchfork bifurcations.
The polynomial control laws designed are given in terms of the original control system. The center manifold theory is used
to simplify the analysis to dimension one. Finally, the results obtained are applied to two underactuated mechanical systems:
the pendubot and the pendulum of Furuta. 相似文献
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(N) . In this article, it is shown that the dynamics near meandering spiral waves or other patterns is determined by a finite-dimensional
vector field that has a certain skew-product structure over the group SESE(N) . This generalizes our earlier work on center-manifold theory near rigidly rotating spiral waves to meandering spirals. In
particular, for meandering spirals, it is much more sophisticated to extract the aforementioned skew-product structure since
spatio-temporal rather than only spatial symmetries have to be accounted for. Another difficulty is that the action of the
Euclidean symmetry group on the underlying function space is not differentiable, and in fact may be discontinuous. Using this
center-manifold reduction, Hopf bifurcations and periodic forcing of spiral waves are then investigated. The results explain
the transitions to patterns with two or more temporal frequencies that have been observed in various experiments and numerical
simulations.
Received December 8, 1997; accepted May 19, 1996 相似文献
16.
Bifurcations for a predator-prey system with two delays 总被引:2,自引:0,他引:2
In this paper, a predator-prey system with two delays is investigated. By choosing the sum τ of two delays as a bifurcation parameter, we show that Hopf bifurcations can occur as τ crosses some critical values. By deriving the equation describing the flow on the center manifold, we can determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. In addition, special attention is paid to the global continuation of local Hopf bifurcations. Using a global Hopf bifurcation result of [J. Wu, Symmetric functional differential equations and neural networks with memory, Trans. Amer. Math. Soc. 350 (1998) 4799-4838], we may show the global existence of periodic solutions. 相似文献
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Jianke Yang 《Studies in Applied Mathematics》2012,129(2):133-162
Bifurcations of solitary waves are classified for the generalized nonlinear Schrödinger equations with arbitrary nonlinearities and external potentials in arbitrary spatial dimensions. Analytical conditions are derived for three major types of solitary wave bifurcations, namely, saddle‐node, pitchfork, and transcritical bifurcations. Shapes of power diagrams near these bifurcations are also obtained. It is shown that for pitchfork and transcritical bifurcations, their power diagrams look differently from their familiar solution‐bifurcation diagrams. Numerical examples for these three types of bifurcations are given as well. Of these numerical examples, one shows a transcritical bifurcation, which is the first report of transcritical bifurcations in the generalized nonlinear Schrödinger equations. Another shows a power loop phenomenon which contains several saddle‐node bifurcations, and a third example shows double pitchfork bifurcations. These numerical examples are in good agreement with the analytical results. 相似文献
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P. J. Giblin J. P. Warder V. M. Zakalyukin 《Proceedings of the Steklov Institute of Mathematics》2009,267(1):59-75
The bifurcations of so-called affine equidistants for a surface in three-space are classified and described geometrically.
An affine equidistant is formed by the points dividing in a given ratio the segment with the endpoints lying on a given surface
provided that the tangent planes to the surface at these endpoints are parallel. The most interesting case corresponds to
segments near parabolic lines. All singularities turn out to be stable and simple. 相似文献
19.
J.A. Langa 《Journal of Differential Equations》2006,221(1):1-35
In a previous paper we introduced various definitions of stability and instability for non-autonomous differential equations, and applied these to investigate the bifurcations in some simple models. In this paper we present a more systematic theory of local bifurcations in scalar non-autonomous equations. 相似文献
20.
In this paper, we consider a pair of delay-coupled limit-cycle oscillators. Regarding the arithmetical average of two delays
as a parameter, we investigate the effect of time delays on its dynamics. We show that there exist stability switches for
time delays under certain conditions, which do not occur for the corresponding coupled system without time delays. A similar
result has been reported for the same delay by Ramana Reddy et al. (Physica D, 129 [1999]), but in the present paper we give
more detailed and specific conditions determining the amplitude death for different delays. On the other hand, we also investigate
Hopf bifurcations induced by time delays using the normal form theory and center manifold reduction. In the region where the
stability switches may occur, we not only specifically determine the direction of Hopf bifurcations but also show that the
bifurcating periodic solutions are orbitally asymptotically stable. Numerical simulation results are also given to support
the theoretical predictions. 相似文献