特征方程

In addition,the dispersion relation and delay characteristics of the coupled mode in two different YIG films are studied by numerical analogue in the range of inclination angle from 5° to 20°.

本文研究了在倾斜静磁场作用下，双层YIG薄膜波导结构中静磁体波的传播特性，得到了其色散的特征方程，计算了磁场倾角从5°到20°范围内双层波导结构中静磁体波传播的色散关系和延迟特性。

The main contents of this paper are organized as follows. At first, we investi-gate the stability and Hopf bifurcations by analyzing the distribution of the rootsof associated characteristic equation.

本文研究的主要内容为：首先通过分析相应特征方程根的情况，来考察不动点的稳定性及Hopf分支存在性。

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。

Choosing time delay as the control parameter, the stability of trivial equilibrium is discussed by analyzing distribution of the roots of the associated characteristic equation. It is found that Hopf bifurcation occurs from trivial equilibrium when the delay passes through critical values, then the critical values and their relations with system control parameters are obtained.

以时滞量为参数，通过分析对应线性系统特征方程的根的分布，讨论了平凡解的稳定性，得到了平凡解发生Hopf分岔而失稳的临界时滞量以及临界时滞量与系统控制参数的关系。

Then the delay is used in circadian model. Using the delay as a argument, the distribution of the roots of the characteristic equation associated with the model under light is analyzed. Then the stable and Hopf bifurcation condition of the circadian model with delay is obtained.

然后，将时滞引入到昼夜节律系统模型后，以滞量为参数，讨论光照昼夜节律模型线性部分特征方程根的分布情况，得到该系统的稳定性和Hopf分支产生的条件。

By analyzing the distribution of the zeros to the transcendental characteristic equation associated with the trivial.solution,we obtain some- sufficient conditions on the stability and instability of the trivial solution.These results are generalized to n-unit neural networks by means of space decomposition in this Chapter.

在第二章中，我们讨论了不带自反馈与带自反馈的3元环状神经网络系统平凡解所对应超越特征方程的根的分布情况，确定了系统平凡解稳定与不稳定的充分条件，并利用空间分解的方法把相应的结果推广到n元环状神经网络系统。

Secondly, by linearizing the system at the unique positive equilibrium solution and analyzing the associated characteristic equation, it is found that the positive equilibrium solution is asymptotically stable when the delay equals to zero and when it is increased to certain critical value, the positive equilibrium solution will loss the stability and a spatially heterohomogeneous periodic solution will bifurcate from this positive equilibrium solution.

通过在系统唯一的正平衡解处线性化系统和分析相应的特征方程，发现在时滞等于零时该正平衡解是渐近稳定的，当时滞逐渐增大到某个临界值时该正平衡解将失去稳定性而且在该平衡解处分支出空间非齐次的周期解。

Then the eigenvalues of the closed loop system is studied and the necessary and sufficient condition for the closed loop system to be asymptotically stable is derived.

其次，对相应的闭环系统特征方程进行详尽的讨论计算，得到了系统本征值的分布特性，从而利用Lassel 不变原理得到了闭环系统渐近稳定的充分必要条件。

By solving the SturmLiouville eigen-equation in the barycentric coordinate, the generalized sine and cosine functions in the triangular domain are constructed. Properties of these functions are systematically investigated by visualization and theoretical derivation.

本文通过求解重心坐标下的Sturm-Liouville特征方程，构造出了三角区域的广义正弦函数和广义余弦函数，并通过可视化与理论推导相结合的方法系统的研究了这两组函数的性质。

By solving the Sturm-Liouville eigen-equation in the barycentric coordinate, the generalized sine and cosine functions in the triangular domain are constructed. Properties of these functions are systematically investigated by visualization and theoretical derivation.

本文通过求解重心坐标下的Sturm-Liouville特征方程，构造出了三角区域的广义正弦函数和广义余弦函数，并通过可视化与理论推导相结合的方法系统的研究了这两组函数的性质。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失