### Abstract

Recent investigations on the bifurcation behavior of power electronic dc-dc converters hare revealed that most of the observed bifurcations do not belong to generic classes such as saddle-node, period doubling, or Hopf bifurcations. Since these systems yield piecewise smooth maps under stroboscopic sampling, a new class of bifurcations occur in such systems when a fixed point crosses the border between the smooth regions in the state space. In this paper we present a systematic analysis of such bifurcations through a normal form: the piecewise linear approximation in the neighborhood of the border. We show that there can be many qualitatively different types of border collision bifurcations, depending on the parameters of the normal form, We present a partitioning of the parameter space of the normal form showing the regions where different types of bifurcations occur. We then use this theoretical framework to explain the bifurcation behavior of the current programmed boost converter.

Original language | English |
---|---|

Pages (from-to) | 633-643 |

Number of pages | 11 |

Journal | IEEE Transactions on Circuits and Systems Part I: Fundamental Theory and Applications |

Volume | 47 |

Issue number | 5 |

Publication status | Published - May 2000 |

### Keywords

- bifurcation theory
- chaos
- nonlinear dynamics
- power electronics
- border-collision bifurcations
- DC-DC converters
- buck converter
- boost converters
- behavior
- systems

### Cite this

*IEEE Transactions on Circuits and Systems Part I: Fundamental Theory and Applications*,

*47*(5), 633-643.

**Bifurcations in two-dimensional piecewise smooth maps : Theory and applications in switching circuits.** / Banerjee, S ; Ranjan, P ; Grebogi, C .

Research output: Contribution to journal › Article

*IEEE Transactions on Circuits and Systems Part I: Fundamental Theory and Applications*, vol. 47, no. 5, pp. 633-643.

}

TY - JOUR

T1 - Bifurcations in two-dimensional piecewise smooth maps

T2 - Theory and applications in switching circuits

AU - Banerjee, S

AU - Ranjan, P

AU - Grebogi, C

PY - 2000/5

Y1 - 2000/5

N2 - Recent investigations on the bifurcation behavior of power electronic dc-dc converters hare revealed that most of the observed bifurcations do not belong to generic classes such as saddle-node, period doubling, or Hopf bifurcations. Since these systems yield piecewise smooth maps under stroboscopic sampling, a new class of bifurcations occur in such systems when a fixed point crosses the border between the smooth regions in the state space. In this paper we present a systematic analysis of such bifurcations through a normal form: the piecewise linear approximation in the neighborhood of the border. We show that there can be many qualitatively different types of border collision bifurcations, depending on the parameters of the normal form, We present a partitioning of the parameter space of the normal form showing the regions where different types of bifurcations occur. We then use this theoretical framework to explain the bifurcation behavior of the current programmed boost converter.

AB - Recent investigations on the bifurcation behavior of power electronic dc-dc converters hare revealed that most of the observed bifurcations do not belong to generic classes such as saddle-node, period doubling, or Hopf bifurcations. Since these systems yield piecewise smooth maps under stroboscopic sampling, a new class of bifurcations occur in such systems when a fixed point crosses the border between the smooth regions in the state space. In this paper we present a systematic analysis of such bifurcations through a normal form: the piecewise linear approximation in the neighborhood of the border. We show that there can be many qualitatively different types of border collision bifurcations, depending on the parameters of the normal form, We present a partitioning of the parameter space of the normal form showing the regions where different types of bifurcations occur. We then use this theoretical framework to explain the bifurcation behavior of the current programmed boost converter.

KW - bifurcation theory

KW - chaos

KW - nonlinear dynamics

KW - power electronics

KW - border-collision bifurcations

KW - DC-DC converters

KW - buck converter

KW - boost converters

KW - behavior

KW - systems

M3 - Article

VL - 47

SP - 633

EP - 643

JO - IEEE Transactions on Circuits and Systems Part I: Fundamental Theory and Applications

JF - IEEE Transactions on Circuits and Systems Part I: Fundamental Theory and Applications

SN - 1057-7122

IS - 5

ER -