分支

In this thesis, we take the delay r as a bifurcation parameter to investigate the Hopf bifurcation phenomenon in system (1). By analyzing the associated characteristic transcendental equation of system (2), and using the Hopf bifurcation theorem, we obtain one condition for the existence of Hopf bifurcation in system (1). Furthermore, based on the center manifold theorem and the method of normal form, some interesting results about the properties of Hopf bifurcation are obtained, including the direction of Hopf bifurcation and stability of Hopf bifurcating periodic solutions.

我们以时滞T作为分支参数，研究了系统(1)的Hopf分支现象：通过分析系统(2)的特征超越方程，结合利用Hopf分支定理获得了系统(1)的Hopf分支存在的一个条件；利用中心流形定理和正规形方法分析了系统(1)的Hopf分支的性质，包括分支的方向和分支周期解的稳定性。

On the basis of some elementary theories about Galton-Watson branching process, the bisexual Galton-Watson branching process and the branching process with random environment are introduced in the paper.

本文在介绍GW分支过程一些基本理论的基础上，又介绍了两性分支过程模型及随机环境分支过程模型，并以两性分支过程为前提，研究了带配对函数L=x的两性分支过程{Z_n}。

What differ from that of the researchers in the past is the consideration of the direction of Hopf bifurcation with Dirichlet boundary condition , that is, the conditions when the Hopf bifurcation periodic solutions are orbitally asymptotically stable with asymptotic phase.Our basic idea come from the results given by Tang[30]. We adopt the method used by Hassard in the Hopf bifurcation theorem in [24], which is to judge the existence and the direction of Hopf bifurcation, and the stability of the Hopf bifurcation periodic solutions.

与以前的研究者不同的是，本文不仅讨论了在Dirichlet边界条件下系统的Hopf分支在以扩散系数为分支参数的情况下的存在性和分支周期解的空间非齐次性，而且更多的关注了系统在Dirichlet边界条件下Hopf分支解的稳定性及Hopf分支的方向，也即系统定态解在何种条件下，当分支参数如何变化时产生Hopf分支且分支周期解是带渐近位相轨道渐近稳定的。

Firstly, the connection matrices are strongly connected Boolean matrix, it is shown that the maximum length of limit cycles for FBAM is the period index of the product of the connection matrices. Thus, the maximum limit cycle is reachable. Secondly, two strongly connected components are connected by walks, it is proved that the maximum length of limit cycles for FBAM is the max. of the period index of the two strongly connected components if they are prime, otherwise, it is the least common multiple of the two period index. Finally, n strongly connected component are connected in succession, the method for computing the maximum length is described. By different patterns are presented to the networks, diminishing the number of the strongly connected components until only two components.

第一，连接权矩阵为强连通布尔矩阵，此时模糊双向联想记忆网络的最大极限环长度为连接权矩阵乘积的周期指数，从而极限环具有可达性；第二，两个强连通分支有路径连接，此时如果两个强连通分支的周期指数互素，那么网络的最大极限环长度为其最大者，否则，网络的最大极限环长度就等于二者的最小公倍数；第三，n个相邻强连通分支有路径连接，给出了计算最大极限环长度的方法，通过激发模式的变化，逐渐减少强连通分支的个数，直到只有两个分支。

The first to tertiary ramification of portal vein and their significance. The first order branch of portal vein had four patterns: namely, normal branching pattern, 90 cases (90%); trifurcation, 5 cases (5%); independent branching of right posterior branch from main portal vein, 4 cases (4%); and complicated branching pattern, 1 case (1%).

门静脉第一到第三级分支的解剖和变异门静脉第一级分支有四种类型，即正常分支型，90例（90％）；右前支、右后支和左门静脉同时分支型，5例（5％）；右后支独立分支型，4例（4％）；及复杂分支型，1例（1％）。15例（15％）右门静脉不形成单独右后支，而是右后下支P6和右后上支P7分别从右门静脉分出，这种变异并非少见而文献中却很少描述。

Analytic branch amount and branch angle are right produce can influence discovery: Mi Qian is planted increase of number of branch of? of You of that a pavilion or house on a terrace of joyous ǖ of Сざ sew, produce can reduce somewhat, think branch well should not seek overmuch branch amount, with 2~3 branch is advisable; branch angle increases, the yield of much branch well also can increase, but addition extent decrescent.

分析分支数目和分支角度对产能的影响发现：在总分支长度一定的情况下，分支数目增多，产能略有降低，认为分支井不应追求过多的分支数目，以2~3个分支为宜；分支角度增大，多分支井的产能也增大，但增加的幅度变小。

Therefore, based on numerical calculation of a multibranch well's productivity, the influences of the branch angle, branch interspaces and branch length on the gas yield are investigated. The results show that a.

为此，以多分支井产能数值计算方法为基础，研究了多分支井的分支角度、分支间距和分支长度对产能的影响。

For a higher yield, the multibranch well bore should be perpendicular to the direction of maximum principal permeability, b. for a given coalbed methane reservoir, there is an optimal interspace, by which a bigger control area and the interaction among the branches can be obtained, and c. with the extension of the branch, gas yield becomes obviously higher, while the branch length should be an appropriate value on account of the influence of coal bed boundary and wellbore pressure drop. The research results have guiding significance for well pattern optimization and efficient development of coalbed methane gas.

结果发现：为了获得较高的产能，多分支井的井筒应垂直于最大主渗透率方向；对于给定的煤层气藏，存在一个最优的分支间距，既能保证较大的控制面积，又能保证分支间的互相影响；随着分支长度的增高，产气量也显著增大，但是考虑到煤层边界和井筒压降的影响，分支长度也应该有一个比较合理的值。

It is shown that the direction of bifurcation and the stability of the bifurcating periodic solutions of the Euler methods are the same as the direction of bifurcation and the stability of the bifurcating periodic solutions of the original delay differential equation when the stepsize is small enough.

证明当步长充分小时数值Hopf分支的分支方向、分支周期解的稳定性与原方程的Hopf分支的分支方向、分支周期解的稳定性相同。

Therefore, based on numerical calculation of a multi-branch well's productivity, the influences of the branch angle, branch interspaces and branch length on the gas yield are investigated. The results show that a.

为此，以多分支井产能数值计算方法为基础，研究了多分支井的分支角度、分支间距和分支长度对产能的影响。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷