saddle node

Homoclinic Bifurcation and Time-Dependent Bifurcation of Quadratic System with Saddle-Node Bifurcation

具有鞍结分岔的二次系统的同宿和时变分岔

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Based on the principle of the continuation method ( indirect method), it is proposed that this method be used to directly trace 2-dimensional singularity induced, saddle-node and Hopf bifurcations boundary occurring in the differential-algebraic equations ( DAEs) that model power system voltage stability.

基于延拓法的原理，提出应用该方法来直接追踪动态电压稳定微分一代数联立方程中的奇异性、鞍结点和霍普夫等分岔的二维参数边界。

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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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From simulation results, the jump from one periodic to another periodic motion corresponds to Saddle-node bifurcation, and the evolution from period to quasi-period corresponds to Hopf bifurcation.

由结果可以看出，裂纹转子运动在周期解之间的跳跃对应于鞍结分叉；周期到拟周期的变化对应于Hopf分叉；

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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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