### Abstract

Blowout bifurcation in chaotic dynamical systems occurs when a chaotic attractor, lying in some invariant subspace, becomes transversely unstable. We establish quantitative characterization of the blowout bifurcation by unstable periodic orbits embedded in the chaotic attractor. We argue that the bifurcation is mediated by changes in the transverse stability of an infinite number of unstable periodic orbits. There are two distinct groups of periodic orbits: one transversely stable and another transversely unstable. The bifurcation occurs when some properly weighted transverse eigenvalues of these two groups are balanced.

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

Pages (from-to) | R1251-R1254 |

Number of pages | 4 |

Journal | Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 55 |

Issue number | 2 |

Publication status | Published - Feb 1997 |

### Keywords

- ON-OFF INTERMITTENCY
- CHAOTIC ATTRACTORS
- STRANGE ATTRACTORS
- RIDDLED BASINS
- SYSTEMS
- METAMORPHOSES
- DIMENSIONS
- BOUNDARIES
- MOTION

### Cite this

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*55*(2), R1251-R1254.

**Characterization of blowout bifurcation by unstable periodic orbits.** / Nagai, Y ; Lai, Y C ; Lai, Ying-Cheng.

Research output: Contribution to journal › Article

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 55, no. 2, pp. R1251-R1254.

}

TY - JOUR

T1 - Characterization of blowout bifurcation by unstable periodic orbits

AU - Nagai, Y

AU - Lai, Y C

AU - Lai, Ying-Cheng

PY - 1997/2

Y1 - 1997/2

N2 - Blowout bifurcation in chaotic dynamical systems occurs when a chaotic attractor, lying in some invariant subspace, becomes transversely unstable. We establish quantitative characterization of the blowout bifurcation by unstable periodic orbits embedded in the chaotic attractor. We argue that the bifurcation is mediated by changes in the transverse stability of an infinite number of unstable periodic orbits. There are two distinct groups of periodic orbits: one transversely stable and another transversely unstable. The bifurcation occurs when some properly weighted transverse eigenvalues of these two groups are balanced.

AB - Blowout bifurcation in chaotic dynamical systems occurs when a chaotic attractor, lying in some invariant subspace, becomes transversely unstable. We establish quantitative characterization of the blowout bifurcation by unstable periodic orbits embedded in the chaotic attractor. We argue that the bifurcation is mediated by changes in the transverse stability of an infinite number of unstable periodic orbits. There are two distinct groups of periodic orbits: one transversely stable and another transversely unstable. The bifurcation occurs when some properly weighted transverse eigenvalues of these two groups are balanced.

KW - ON-OFF INTERMITTENCY

KW - CHAOTIC ATTRACTORS

KW - STRANGE ATTRACTORS

KW - RIDDLED BASINS

KW - SYSTEMS

KW - METAMORPHOSES

KW - DIMENSIONS

KW - BOUNDARIES

KW - MOTION

M3 - Article

VL - 55

SP - R1251-R1254

JO - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 2

ER -