A Method of Following the Unstable Path Between Two Saddle-Node Bifurcation Points in Nonlinear Dynamic System

Zhang Jiazhong; Hua Jun; Xu Qingyu

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Article Navigation > Applied Mathematics and Mechanics > 1999 > 20(12): 1281-1285

Zhang Jiazhong, Hua Jun, Xu Qingyu. A Method of Following the Unstable Path Between Two Saddle-Node Bifurcation Points in Nonlinear Dynamic System[J]. Applied Mathematics and Mechanics, 1999, 20(12): 1281-1285.

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A Method of Following the Unstable Path Between Two Saddle-Node Bifurcation Points in Nonlinear Dynamic System

School of Architecture Engineering and Mechanics, Xi'an Jiaotong University, Xi'an 710049, P R China

Received Date: 1998-09-14
Rev Recd Date: 1999-04-13
Publish Date: 1999-12-15

Abstract

Abstract

A computation algorithm based on the Poincar Mapping in combination with Pseudo-Arc Length Continuation Method is presented for calculating the unstable response with saddle-node bifurcation,and the singularity,which occurs using the general continuation method combined with Poincar Mapping to follow the path,is also proved. A normalization equation can be introduced to avoid the singularity in the process of iteration, and a new iteration algorithm will be presented too.There will be two directions in which the path can be continued at each point,but only one can be used,the method of determining the direction will be presented in the paper.It can be concluded that this method is effective in analysis of non-linear dynamic system with saddle-node bifurcations.
- nonlinear dynamic system,
- bifurcation,
- stability

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References(4)

References

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