分岔

In Chapter 3,we focus on three-unit neural networks without self-feedback.Finding out the way the eigenvalues with positive real parts changing,we consider bifurcation near the trivial solution.

在第三章中，我们主要讨论不带自反馈的3元环状神经网络系统的平凡解对应特征方程的正实部根个数的变化规律以及该系统在平凡解附近的分岔性质。

The cavitated bifurcation equation that describes cavity formation and growth in the interior of the sphere is obtained. It is proved that there exists a unique bifurcation point on the trivial solution of the cavitated bifurcation equation.

本文利用分岔理论和动力学理论中的基本观点、方法和结论，对具有缺陷的超弹性材科组成的球体内部的空穴生成和增长的拟静态问题以及空穴生成后随时间的运动规律等方面进行了系统的研究，得到了一些新的结论，同时给出了相应的数值分析。

In life, we need turnoff confidence, we need to, we need to be strong.

在人生的分岔路口，我们需要自信，我们需要努力，我们需要将强。

Bifurcation diagram changed with different speed is drawn to analyze the course of the system from steady state to unsteady in order to research the influence of seal to the nonlinear characteristic of rotor.

根据给出的系统随转速变化的分岔图，描述系统由稳定到失稳的过程，分析系统中可能出现的各种运动，研究密封对转子非线性动力特性的影响。

Transfer change from a steady state to an unsteady with the increase of Ra. Further ,the numerical solution ob2

数值解出现了分岔，流动和换热随 Ra 的增大从稳态转变为非稳态；在 Ra 为104 时采用2 种不同的初始条

In Chapter 2, we first introduce the related content of vector field, degenerate equilibrium and its bifurcations.

在第二章，我们首先一般地介绍了向量场、退化奇点及其邻域内发生的分岔等相关内容。

These changes are called bifurcations. If bifurcations or even a versal unfolding are given, all physical phenomena of this system are clear.

弄清了系统的分岔甚至给出了它的普适开折，该系统所发生的所有物理现象都将昭然若示。

Biological dynamic system; Degenerate equilibrium; Generalized normal sector; Periodic solution; Bifurcation; Versal unfolding

基础科学，数学，动力系统理论生物动力系统；退化奇点；广义正常区域；周期解；分岔；普适开折

Degenerate equilibrium; generalized normal sector; bifurcation; codimension; versal unfolding; heteroclinic loop.

基础科学，数学，数学分析退化奇点；广义正常区域；分岔；余维；普适开折；异宿轨

The results show that,the control of delaying period-doubling bifurcations and unstable periodic orbits in a chaotic attracter of the AOB system is effectively realized,and other stable periodic orbits 2np、3mp and 2np×3mp are obtained by adjusting the control parameters.

仿真模拟显示，通过选择恰当的控制参数，有效地实现了声光双稳系统中倍周期分岔的延迟控制和混沌吸引子中原不稳定周期轨道的稳定控制，同时，还可以将系统控制在2np、3mp 和2np×3mp这样其它任意所需的周期轨道上。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。