再構成定理を用いたトリー解析

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In this paper, chaotic properties of electric discharge pulses accompanied with trees developing from a needle-plane electrode system in PE under AC voltage application, and together with fractal properties of the tree patterns are discussed with the Theorem of Reconstructions presented by Takens and fractal theories. The results obtained were : The two dimensional attractor reconstructed by the electric current pulses accompanied with tree developments consisted of plus and minus ones corresponding to plus and minus polarities of the current pulses. The attractor had a fractal property and the dimension D was equal to 1.439. Thus, a chaotic property was obtained for this attractor. It was obtained a relation between the attractor and the developments of tree patterns such that trees developed rapidly when the diameter of the attractor was large and in reciprocal the diameter almost unchanged when the tree developments was local and small. The similar exponent λ_q of the current pulses increased monotonously with moment order q.
東海大学の論文