1994 Fiscal Year Final Research Report Summary
Applications of Chaos and bifurcations in delayd differential equations
| Project/Area Number |
05836004
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
非線形科学
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| Research Institution | University of Tsukuba |
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Principal Investigator |
TOKUNAGA Ryuji Insti.of Inf.Sci.and Elec.University of Tsukuba assistant professor, 電子・情報工学系, 助教授 (30212070)
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| Co-Investigator(Kenkyū-buntansha) |
HIRAI Yuzo Insti.of Inf.Sci.and Elec.professor, 電子・情報工学系, 教授 (80114122)
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| Project Period (FY) |
1993 – 1994
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| Keywords | chaos / bifurcations / learning / prediction / non lnear / neural networks / bifurcation diagram / parameterized family |
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| Research Abstract |
The objective of this research is to study and develop applications of chaos and bifurcations of delayd differential equations.
In the first stage, a delayd differential system with back propagation learning algorithm is applied to deterministic nonlinear prediction. Since its degree of freedom is infinite, very complicated patterns can be learned and generated by the delayd differential systems. The prediction system is tested against several chaotic dynamical systems in order to show its prediction capabilities. [1]
In the second stage, using the proposed system, irregular vibrations in the Japanese vowel sounds are investigated in the light of fractal dimension, Lyapnov exponents, and KS-entropy. Consequently, numerical evidence which suggests their relationship with deterministic chaos are obtained. [2]
In the third srage, a novel inverse problem for chaotic dynamics is formulated and studied. And propose an algorithm to reconstruct qualitatively similar parametrized family of dynamical systems only from several time-waveforms measured from unknown parametrized family of dynamical systems. This algorithm is essentially based on nonlinear prediction technique and principal component analysis. In order to show its capability, it is tested against several parametrized family of discrete dynamical systems. [3][4][5]
In the fourth stage, proposed algorithm is extended, and applied to a time-continuous system. Here, effect of observational noise is also investigated, and its robustness is numerically confirmed. Since this improved algorithm is extremely simple, it is possible to apply this technique to system indentification and time-waveform recognition of unknown chaotic dynamics.
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