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The distribution of the associated characteristic equation roots is given according to the polynomial theorem, and the conditions for ensuring the existence of Hopf bifurcation are obtained. The obtained result is applied to chaotic control.

利用多项式理论给出了其特征方程根的分布，得到了Hopf分岔产生的条件，并将结果应用到混沌神经网络的控制中。

Algorithm application of neural networks.Ⅲ Implementation of neuro-computers. The main contribution of the dissertation can be summarized as follows: 1 Hopf bifurcation of three kind of neural networks are discussed in detail, including type of discrete time delay, type of time delay with weak kernel and strong kernel as well as the proof of existence of bifurcation. Other problems such as asymptotic stability of bifurcation periodic solution, algorithm of determining the bifurcation direction, asymptotic stability and style of periodic solution are also studied. The average time delay is chosen as the bifurcation parameter, phenomena pertinent to system states of the continuous time delay network with strong kernel evolving from stable to oscillating, then back to stable again are observed.

论文的主要创新之处可以归纳如下： 1）针对目前国内外对神经网络的分岔研究较少的情况，论文中详细讨论了带离散时延神经网络、带弱核的连续时延神经网络、带连续分布时延且具有强核的神经网络的Hopf分岔现象，从理论上证明了Hopf分岔的存在性，并研究了分岔周期解的渐近稳定性，得到了确定周期解的渐近稳定性、分岔方向、周期解的渐近形式的算法；用平均时延作为分岔参数，发现带强核的连续时延神经网络中存在着系统的状态由稳定变化到振荡现象，当继续增加平均时延参数时，又从振荡变为稳定这一特殊的动力学现象。

In Arcade Ball the player's consciousness is bifurcate: one half turns into a small but very quick ball, and the other one - into an imperturbable platform which begins to order the light-minded ball about in every possible way and thrash it.

在商场球球员的意识是分岔：一一半变成了一个小但很快速球，和其他一-寻找到了一个i mperturbable平台开始，为了因志同道合的球约在一切可能的方式和敲击。

The experiments of neuronal pacemaker show typical bifurcations from period 1 to period 5 with stochastic bursting patterns. A discontinuous map of the slow variable in Chay model which captures the essential characters of the period-adding bifurcation scenario is constructed in this thesis.

在神经起步点实验中展示了伴有随机簇放电的从周期1到周期5的典型分岔，本文在把握加周期分岔的根本特征的基础上构造了Chay模型中慢变量的不连续映射。

The deterministic neuronal firing model could simulate only the period adding bifurcation scenario in which period n bursting was changed into period n+1 bursting directly. The period adding bifurcation scenario and the new firing pattern similar to the experiment could be simulated in the stochastic Chay model.

确定性神经放电理论模型只能模拟周期n节律直接到周期n+1节律的加周期分岔序列；而随机Chay模型可以模拟实验中的加周期分岔过程和新节律。

In particular, the system generates bifurcation when 2c-a=0, and then the stable knot bifurcates a hyperbolic saddle point and stable convergence, which is so-called Pitchfork bifurcation. From 2c-a≤0 to 2c-a≥0, the attracting set A of the system is changed from single point to the union set of two different old orbits.

系统在2c-a=0时产生分岔，其稳定的结点分岔出一双曲鞍点和两个稳定的汇，这就是Pitchfork分岔，可见在2c-a≤0变化到2c-a≥0时，吸引集A从单点集变成为连接P和P的两异宿轨道的并。

In this thesis,the voltage stability boundary is the combined boundary which correspond to Saddle-node bifurcations and Hopf bifurcations.The closest Hopf bifurcation point is found through the proposed iterative method under the assumption that the Hopf hypersurface is continuous and convex.

因此在本论文中，在多维参数空间下，将稳定边界推广到鞍点和Hopf分岔点构成的混合稳定边界，探索性寻求Hopf分岔超平面的法向量，采用迭代算法求取系统发生最近振荡型电压失稳的负荷增长方式。

Furthermore, the periodicity of the phenomena and the route from bifurcation to chaos are also investigated in detail.

同时，详细研究了系统由分岔到混沌的发展过程。

I therefore diverted the present Discourse between me and my Man, rising up hastily, as upon some sudden Occasion of going out; then sending him for something a good way off, I seriously pray'd to God that he would enable me to instruct savingly this poor Savage, assisting by his Spirit the Heart of the poor ignorant Creature, to receive the Light of the Knowledge of God in Christ, reconciling him to himself, and would guide me to speak so to him from the Word of God, as his Conscience might be convinc'd, hid Eyes open'd, and his Soul sav'd.

因此，我马上把我和星期五之间的谈话岔到别的事情上去。我匆匆忙忙站起来，仿佛突然想到一件什么要紧的事情，必须出去一下。同时，我又找了一个借口，把他差到一个相当远的地方去办件什么事。

The characteristics of Hopf bifurcation from the origin, including the existence condition, the direction as well as the stability of bifurcating periodic solutions are discussed in detail, which can be demonstrated by the numerical simulations.

讨论了快慢两时间尺度下超混沌Lorenz系统原点的稳定性问题，分析了原点的Hopf分岔，包括Hopf分岔的存在性，分岔方向以及分岔周期解的稳定性等问题，并用数值例子对所得到的结果加以验证。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。