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|Title:||Connecting border collision with saddle-node bifurcation in switched dynamical systems|
Tse, C. K. Michael
Switched dynamical systems
|Source:||IEEE transactions on circuits and systems. II, Express briefs, Sept. 2005, v. 52, no. 9, p. 581-585.|
|Abstract:||Switched dynamical systems are known to exhibit border collision, in which a particular operation is terminated and a new operation is assumed as one or more parameters are varied. In this brief, we report a subtle relation between border collision and saddle-node bifurcation in such systems. Our main finding is that the border collision and the saddle-node bifurcation are actually linked together by unstable solutions which have been generated from the same saddle-node bifurcation. Since unstable solutions are not observable directly, such a subtle connection has not been known. This also explains why border collision manifests itself as a “jump” from an original stable operation to a new stable operation. Furthermore, as the saddle-node bifurcation and the border collision merge tangentially, the connection shortens and eventually vanishes, resulting in an apparently continuous transition at border collision in lieu of a “jump.” In this brief, we describe an effective method to track solutions regardless of their stability, allowing the subtle phenomenon to be uncovered.|
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|Appears in Collections:||EIE Journal/Magazine Articles|
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