2000 Fiscal Year Final Research Report Summary
A Fundamental Study on Dynamics and Control of Complex Systems
| Project/Area Number |
10650236
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Dynamics/Control
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| Research Institution | Gifu University |
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Principal Investigator |
YAGASAKI Kazuyuki Gifu University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (40200472)
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| Project Period (FY) |
1998 – 2000
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| Keywords | Complex System / Chaos / Coupled Oscillator / Bifurcation / Chaos Control / Dynamical Systems Theory / Hawiltonian System |
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| Research Abstract |
In this research, as a fundamental study on dynamics and control of complex systems like atmosphere, life and economic systems, analytical techniques for nonlinear behavior and chaos control methods in coupled oscillators were established as follows.
1.For general two-degree-of-freedom dissipative systems with periodic forcing, a theoretical technique to analyze homoclinic and heteroclinic behavior for resonant periodic orbits was proposed and a mechanism for chaos was described.
2.For multi-degree-of-freedom Hamiltonian systems with saddle-centers, theoretical techniques to analyze homoclinic and heteroclinic behavior for periodic orbits and invariant tori near the saddle-centers were developed. Applying these techniques, we describe complicated behavior in an infinite-degree-of-freedom model for an unforced and undamped, buckled beam.
3.A package of the computer algebra system, Mathematica, to implement necessary computations for the higher-order averaging method, and a driver to a computer software called AUTO for numerical analysis of homoclinic and heteroclinic behavior were developed. Their usefulness was demonstrated for several examples.
4.Nonlinear behavior in a forced, simple pendulum and coupled pendula was analyzed theoretically, and the theoretical results were demonstrated in numerical simulations and experiments. Moreover, a two-link robot manipulator was theoretically and numerically proven to exhibit complicated behavior
5. Applying improved versions of delayed and external feedback, we performed chaos control in a forced, simple pendulum and coupled pendula, and demonstrated their effectiveness under an influence of noise in numerical simulations and experiments.
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