Nonlinear Circuit in Complex Time : Case of Phase-Locked Loops (Special Section of Letters Selected from the 1993 IEICE Fall Conference)
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概要
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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 neighbourhood 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 infinitly 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-integrability 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 equation of PLL.
- 1993-12-25
著者
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Horiuchi Kazuo
the 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 Kazuo
The 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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