Analytic Structure of Phase-Locked Loops in Complex Time (Special Section on Nonlinear Theory and Its Applications)
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概要
- 論文の詳細を見る
The analytic structure of the governing equation for a 2nd order Phase-Locked Loops (PLL) is studied in the complex time plane. By a local reduction of the PLL equation to the Ricatti equation, the PLL equation is analytically shown to have singularities which form a fractal structure in the complex time plane. Such a fractal structure of complex time sigularities is known to be characteristic for nonintegrable, especially chaotic systems. On the other hand, a direct numerical detection of the complex time singularities is performed to verify the fractal structure. The numerical results show the reality of complex time singularities and the fractal structure of singularities on a curve.
- 1994-11-25
著者
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Tanaka Hisa-aki
School Of Science And Engineering Waseda University
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Tanaka Hisa-aki
The School Of Science And Engineering Waseda University
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Horiuchi K
Waseda Univ. Tokyo Jpn
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Horiuchi Kazuo
School of Science and Engineering, Waseda University
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Matsuda T
Ntt Optical Network Systems Lab. Yokosuka‐shi Jpn
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Matsuda Toshiya
NTT Transmission Laboratories
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Horiuchi Kazuo
School Of Science And Engineering Waseda University
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