1999 Fiscal Year Final Research Report Summary
Variety of dynamics in high-dimensional chaotic dynamical systems
| Project/Area Number |
10440054
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | HOKKAIDO UNIVERSITY |
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Principal Investigator |
TSUD Ichiro Hokkaido Univ., Grad. School of Science, Pro., 大学院・理学研究科, 教授 (10207384)
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| Co-Investigator(Kenkyū-buntansha) |
TSUJII Masato Hokkaido Univ., Grad. School of Science, Asso. Pro., 大学院・理学研究科, 助教授 (20251598)
NAMIKI Takao Hokkaido Univ., Grad. School of Science, Assi., 大学院・理学研究科, 助手 (40271712)
MATSUMOTO Kenji Hokkaido Univ., Grad. School of Science, Asso. Pro., 大学院・理学研究科, 助教授 (80183953)
KOBAYASHI Ryo Hokkaido Univ., Res. Inst. Of Electronic Science, Asso. Pro., 電子科学研究所, 助教授 (60153657)
NISHIURA Yasumasa Hokkaido Univ., Res. Inst. Of Electronic Science, Pro., 電子科学研究所, 教授 (00131277)
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| Project Period (FY) |
1998 – 1999
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| Keywords | Chaotic itinerancy / Milnor attractor / Saddle-node bifurcations / Basin structure / Homoclinic tangency |
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| Research Abstract |
The Variety of dynamics in high-dimensional dynamical systems can be observed in both actual and virtual (computer) experiments. It may be identified as a transient motion. A typical phenomenon has been found. The head investigator of this project found chaotic itinerancy in nonequilibrium neural networks, ten years ago. Recently the investigators of this project found a complex transient motion in reaction-diffusion systems, which is derived from a simultaneous annihilation of many pairs of saddle and node. The purpose of this project is to investigate a mechanism of chaotic itinerancy in relation with a creation and annihilation of saddle-node. We observed in computer experiments that a quasiattractor which we called an attractor ruin can be described by a Milnor attractor. Introducing a bifurcation parameter and changing it, we investigated a continuity of a coupled Milnor attractor system to a coupled saddle-node system. Consequently, we found the continuity of these two systems. Furthermore, we found riddled basin boundaries even in the neighborhood of the critical point approached from the case of coupled saddle-node. Therefore, it is plausible to state that the riddled basin boundaries become chaotic orbits that link Milnor attractors.
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