A subtle link in switched dynamical systems: saddle-node bifurcation meets border collision

— 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 paper, 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 relation has not been known. In this paper, we describe an effective method to track solutions regardless of their stability, allowing the subtle phenomenon to be uncovered. Two typical DC-DC converters are observed to verify our finding.1

• Type: Conference
• Year: 2005
• Where: ISCAS
• Authors: Yue Ma, Hiroshi Kawakami, Chi K. Michael Tse, Takuji Kousaka
• Keywords: Border Collision, ISCAS 2005, Saddle-node Bifurcation, Subtle Relation