bifurcation point

The point at which branching of the graph occurs is called a bifurcation point and corresponds to a critical value of the load.

图上发生分叉处的点叫分支点，它相当于荷载的临界值。

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Numerical algorithm for determining Hopf bifurcation point of nonlinear system

确定非线性系统Hopf分岔点的数值方法

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A Direct Method for Computing Hopf Bifurcation Point in Power System Dynamic Voltage Stability

以简化直接法求解电力系统动态电压稳定Hopf分岔点

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The tangent stiffness matrix is obtained from the engineering strain and the principle for determining the limit point and bifurcation point is given.

由工程应变推导出几何非线性的切线刚度矩阵，并给出判断分歧点与极限点的准则，最后用一数值例题说明该方法的分析过程。

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One factor is a new set of characteristic equations for the saddle-node bifurcation point which is of dimension n+ 1, instead of 2n+ 1, which is traditionally required in n-dimensional decoupled paramter-dependent power flow equations.

特点是：①对于一n维潮流方程，计算其鞍型分叉点所需求解的是n＋1维特征方程，而不是常规求解方法中的2n+1维特征方程。

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A new computation method for saddle-node bifurcation point of power system

一种新的电力系统鞍型分叉点计算方法

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Roadway crossing point is the intersection of roadway or bifurcation of roadway.

巷道交岔点是指矿井中巷道交会或分岔处的一段巷道。

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The Extended System of Simple Bifurcation Point of the Navier-Stokes Equations

Navier-Stokes方程简单分歧点的扩充系统

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In this paper, with the Louts criterion for Hopf bifurcation, the Hopf bifurcation point of the nonlinear systems and the corresponding frequency at this point can be obtained directly, which overcomes the drawback of the traditional method involving much computation for systems' Jacobian matrix.

通过引入Hopf分岔的劳斯判据，可直接求得非线性系统的Hopf分岔点以及系统振荡的频率，克服了以往方法因计算系统Jacobian矩阵的计算量大的缺点。

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The extended systems for computing simple high order bifurcation point are constructed.

构造了计算简单高阶分歧点的扩充系统。

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The Hopf bifurcation behavior from the zero equilibrium, which is a saddle point, is created under the combination control of linear and nonlinear feedback.

在线性与非线性状态反馈控制共同作用下，在该系统原为鞍点的零平衡点上，创建了稳定的Hopf分岔行为。

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Characteristic of nonlinear system stochastic resonance in the neighbourhood of bifurcation point

非线性动力系统分岔点邻域内随机共振的特性

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the results of the numerical solution show that the overall behaviour of the material and the critical strain of the shear band bifurcation point are closely related to the size of the voids and the parameter a of controlled loading.

计算结果表明，宏观材料的软化、塑性可膨胀性、内部损伤的发展以及剪切分叉的临界应变值等，都与加载参数α、原始空洞尺度有着密切的关系。

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We have reached another bifurcation point in history.

我们再次来到了历史上的分歧点.

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A Numerical Method for Hopf Bifurcation Point in Ordinary Differential Equations

关于常微分方程Hopf分支点的一种数值计算方法

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