## Abstract

We study in detail complex structures of homoclinic bifurcations in a three-dimensional rate-equation model of a semiconductor laser receiving optically injected light of amplitude K and frequency detuning ω. Specifically, we find and follow in the (K, ω)-plane curves of n-homoclinic bifurcations, where a saddle-focus is connected to itself at the nth return to a neighbourhood of the saddle. We reveal an intricate interplay of codimension-two double-homoclinic and T-point bifurcations. Furthermore, we study how the bifurcation diagram changes with an additional parameter, the so-called linewidth enhancement factor α of the laser. In particular, we find folds (minima) of T-point bifurcation and double-homoclinic bifurcation curves, which are accumulated by infinitely many changes of the bifurcation diagram due to transitions through singularities of surfaces of homoclinic bifurcations.

The injection laser emerges as a system that allows one to study codimension-two bifurcations of n-homoclinic orbits in a concrete vector field. At the same time, the bifurcation diagram in the (K, ω)-plane is of physical relevance. An example is the identification of regions, and their dependence on the parameter α, of multi-pulse excitability where the laser reacts to a single small perturbation by sending out n pulses.

The injection laser emerges as a system that allows one to study codimension-two bifurcations of n-homoclinic orbits in a concrete vector field. At the same time, the bifurcation diagram in the (K, ω)-plane is of physical relevance. An example is the identification of regions, and their dependence on the parameter α, of multi-pulse excitability where the laser reacts to a single small perturbation by sending out n pulses.

Original language | English |
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Pages (from-to) | 1095-1120 |

Number of pages | 26 |

Journal | Nonlinearity |

Volume | 18 |

Issue number | 3 |

Early online date | 9 Feb 2005 |

DOIs | |

Publication status | Published - May 2005 |