### Abstract

This paper presents a theory for characterization of the blowout bifurcation by periodic orbits. Blowout bifurcation in chaotic systems occurs when a chaotic attractor, lying in some symmetric invariant subspace, becomes transversely unstable. We present an analysis and numerical results that indicate that the bifurcation is mediated by changes in the transverse stability of an infinite number of unstable periodic orbits embedded in the chaotic attractor. 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. Our results thus categorize the blowout bifurcation as a unique type of bifurcation that involves an infinite number of periodic orbits, in contrast to most previously known bifurcations that are mediated by only a finite number of periodic orbits.

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

Pages (from-to) | 4031-4041 |

Number of pages | 11 |

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

Volume | 56 |

Issue number | 4 |

Publication status | Published - Oct 1997 |

### Keywords

- ON-OFF INTERMITTENCY
- SYMMETRY-BREAKING BIFURCATION
- CHAOTIC DYNAMICAL-SYSTEMS
- STRANGE ATTRACTORS
- BASIN BOUNDARIES
- RIDDLED BASINS
- INTERMINGLED BASINS
- SYNCHRONIZED CHAOS
- OSCILLATORS
- METAMORPHOSES

### Cite this

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

*56*(4), 4031-4041.

**Periodic-orbit theory of the blowout bifurcation.** / 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. 56, no. 4, pp. 4031-4041.

}

TY - JOUR

T1 - Periodic-orbit theory of the blowout bifurcation

AU - Nagai, Y

AU - Lai, Y C

AU - Lai, Ying-Cheng

PY - 1997/10

Y1 - 1997/10

N2 - This paper presents a theory for characterization of the blowout bifurcation by periodic orbits. Blowout bifurcation in chaotic systems occurs when a chaotic attractor, lying in some symmetric invariant subspace, becomes transversely unstable. We present an analysis and numerical results that indicate that the bifurcation is mediated by changes in the transverse stability of an infinite number of unstable periodic orbits embedded in the chaotic attractor. 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. Our results thus categorize the blowout bifurcation as a unique type of bifurcation that involves an infinite number of periodic orbits, in contrast to most previously known bifurcations that are mediated by only a finite number of periodic orbits.

AB - This paper presents a theory for characterization of the blowout bifurcation by periodic orbits. Blowout bifurcation in chaotic systems occurs when a chaotic attractor, lying in some symmetric invariant subspace, becomes transversely unstable. We present an analysis and numerical results that indicate that the bifurcation is mediated by changes in the transverse stability of an infinite number of unstable periodic orbits embedded in the chaotic attractor. 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. Our results thus categorize the blowout bifurcation as a unique type of bifurcation that involves an infinite number of periodic orbits, in contrast to most previously known bifurcations that are mediated by only a finite number of periodic orbits.

KW - ON-OFF INTERMITTENCY

KW - SYMMETRY-BREAKING BIFURCATION

KW - CHAOTIC DYNAMICAL-SYSTEMS

KW - STRANGE ATTRACTORS

KW - BASIN BOUNDARIES

KW - RIDDLED BASINS

KW - INTERMINGLED BASINS

KW - SYNCHRONIZED CHAOS

KW - OSCILLATORS

KW - METAMORPHOSES

M3 - Article

VL - 56

SP - 4031

EP - 4041

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 - 4

ER -