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| DETECTING AND SWITCHING METHODS FOR SIMPLE BIFURCATION POINTS |
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Citation： |
Shi Miaogen.DETECTING AND SWITCHING METHODS FOR SIMPLE BIFURCATION POINTS[J].Chinese Annals of Mathematics B,1988,9(3):351~361 |
| Page view： 836
Net amount： 676 |
Authors： |
Shi Miaogen; |
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| Abstract： |
For a finite-dimensional equation $\[G(y,t) = 0\]$, where $\[G:D \subset {R^{n + 1}} \to {R^n}\]$, suppose that on
its primary solution curve there is a simple bifurcation point $\[{x^*} = ({y^*},{t^*})\]$ from where a secondary solution enrve is branching off. Then during the trace process of the primary curve by a continuation method, it is always necessary to locate $\[{x^*}\]$ and to find another point on the secondary curve for switching to trace it. This paper presents a proof of a practical criterion for detecting simple bifurcation points and constructs a simplified perturbation algorithm for switching branches. The convergence result of the algorithm is also given.
Our experiments show that the new method is more effective than other perturbation methods, especially for large scale problems. |
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