### Abstract

Quasiperiodical motion in the complex Lorenz equations describing a detuned laser is shown to consist of twin oscillations: the first oscillation originates from Hopf bifurcation and the second is a parastic oscillation of the first one. Equations for the twin asymptotic oscillations are analytically derived in the center manifold, showing explicitly the parastic property of the second oscillation: its frequency is proportional to the square of the amplitude of the first one. The phase of the second oscillation shows also certain anholonomy which is very similar to the characteristics of Berry's phase. Numerical results show further that the first oscillation follows the sequence of bifurcations from simple periodic through period-doubling to chaos, as one continuously increases the control parameter, whereas the frequency of the parastic oscillation does not change qualitatively during the bifurcation process.

Original language | English (US) |
---|---|

Pages (from-to) | 457-461 |

Number of pages | 5 |

Journal | Zeitschrift für Physik B Condensed Matter |

Volume | 81 |

Issue number | 3 |

DOIs | |

State | Published - Oct 1990 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Condensed Matter Physics
- Electronic, Optical and Magnetic Materials

### Cite this

**Quasiperiodicity involving twin oscillations in the complex Lorenz equations describing a detuned laser.** / Ning, Cun-Zheng; Haken, Hermann.

Research output: Contribution to journal › Article

*Zeitschrift für Physik B Condensed Matter*, vol. 81, no. 3, pp. 457-461. https://doi.org/10.1007/BF01390829

}

TY - JOUR

T1 - Quasiperiodicity involving twin oscillations in the complex Lorenz equations describing a detuned laser

AU - Ning, Cun-Zheng

AU - Haken, Hermann

PY - 1990/10

Y1 - 1990/10

N2 - Quasiperiodical motion in the complex Lorenz equations describing a detuned laser is shown to consist of twin oscillations: the first oscillation originates from Hopf bifurcation and the second is a parastic oscillation of the first one. Equations for the twin asymptotic oscillations are analytically derived in the center manifold, showing explicitly the parastic property of the second oscillation: its frequency is proportional to the square of the amplitude of the first one. The phase of the second oscillation shows also certain anholonomy which is very similar to the characteristics of Berry's phase. Numerical results show further that the first oscillation follows the sequence of bifurcations from simple periodic through period-doubling to chaos, as one continuously increases the control parameter, whereas the frequency of the parastic oscillation does not change qualitatively during the bifurcation process.

AB - Quasiperiodical motion in the complex Lorenz equations describing a detuned laser is shown to consist of twin oscillations: the first oscillation originates from Hopf bifurcation and the second is a parastic oscillation of the first one. Equations for the twin asymptotic oscillations are analytically derived in the center manifold, showing explicitly the parastic property of the second oscillation: its frequency is proportional to the square of the amplitude of the first one. The phase of the second oscillation shows also certain anholonomy which is very similar to the characteristics of Berry's phase. Numerical results show further that the first oscillation follows the sequence of bifurcations from simple periodic through period-doubling to chaos, as one continuously increases the control parameter, whereas the frequency of the parastic oscillation does not change qualitatively during the bifurcation process.

UR - http://www.scopus.com/inward/record.url?scp=0040249385&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040249385&partnerID=8YFLogxK

U2 - 10.1007/BF01390829

DO - 10.1007/BF01390829

M3 - Article

AN - SCOPUS:0040249385

VL - 81

SP - 457

EP - 461

JO - Zeitschrift für Physik B Condensed Matter and Quanta

JF - Zeitschrift für Physik B Condensed Matter and Quanta

SN - 0340-224X

IS - 3

ER -