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

Yue Ma; Chi K. Tsey; Takuji Kousakaz; Hiroshi Kawakami

doi:10.1109/ISCAS.2005.1466019

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

Yue Ma, Chi K. Tsey, Takuji Kousakaz, Hiroshi Kawakami

The Hong Kong Polytechnic University

Research output: Journal article publication › Conference article › Academic research › peer-review

4 Citations (Scopus)

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 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.

Original language	English
Article number	1466019
Pages (from-to)	6050-6053
Number of pages	4
Journal	Proceedings - IEEE International Symposium on Circuits and Systems
DOIs	https://doi.org/10.1109/ISCAS.2005.1466019
Publication status	Published - 1 Dec 2005
Event	IEEE International Symposium on Circuits and Systems 2005, ISCAS 2005 - Kobe, Japan Duration: 23 May 2005 → 26 May 2005

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/ISCAS.2005.1466019

Cite this

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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 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.",

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AU - Ma, Yue

AU - Tsey, Chi K.

AU - Kousakaz, Takuji

AU - Kawakami, Hiroshi

PY - 2005/12/1

Y1 - 2005/12/1

N2 - 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.

AB - 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.

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M3 - Conference article

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EP - 6053

JO - Proceedings - IEEE International Symposium on Circuits and Systems

JF - Proceedings - IEEE International Symposium on Circuits and Systems

M1 - 1466019

T2 - IEEE International Symposium on Circuits and Systems 2005, ISCAS 2005

Y2 - 23 May 2005 through 26 May 2005

ER -

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

Abstract

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