## 抄録

We analyze the nonlinear dynamics of PLL from the complex' singularity structure by introducing the complex time. The most important results which we have obtained in this work are as follow: (1) From the psi-series expansion of the solution, the local behavior in the neighborhood of a movable singularity is mapped onto an integrable differential equation: the Ricatti equation. (2) From the movable pole of the Ricatti equation, a set of infinitely clustered singularities about a movable singularity is shown to exist for the equation of PLL by the multivalued mapping. The above results are interesting because the clustering and/or the fractal distribution of singularities is known to be a characteristic feature of the non-integrabilities or chaos. By using the method in this letter, we can present a circumstantial evidence for chaotic dynamics without assuming any small parameters in the in the equation of PLL.

本文言語 | English |
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ページ（範囲） | 2055-2058 |

ページ数 | 4 |

ジャーナル | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

巻 | E76-A |

号 | 12 |

出版ステータス | Published - 1993 12月 1 |

## ASJC Scopus subject areas

- 信号処理
- コンピュータ グラフィックスおよびコンピュータ支援設計
- 電子工学および電気工学
- 応用数学