2001 Fiscal Year Final Research Report Summary
A study about complex motion caused by hierarchical structure and intermittency, in nonlinear dynamical system with large degree of freedom
| Project/Area Number |
12834012
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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 Institution | Kagoshima University |
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Principal Investigator |
HATA Hiroki Kagoshima University, Faculty of Science, Associate Professor, 理学部, 助教授 (30212145)
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| Co-Investigator(Kenkyū-buntansha) |
INOUE Masayoshi Kagoshima University, Faculty of Science, Professor, 理学部, 教授 (80041234)
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| Project Period (FY) |
2000 – 2001
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| Keywords | high dimensional chaos / On-off intermittency / dynamical glass / chaotic itinerancy / anomalous diffusion / Hamilton chaos / generalized shift / volcano |
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| Research Abstract |
Various hierarchical structures and motion hide in nonlinear dynamical systems, and so it is an important problem to build new methodology and general idea to understand it. We paid our attention to the hierarchical structure of invariant manifolds in nonlinear dynamical systems with the large degree of freedom as its approach, and understanding the motion theoretically and numerically is our aim of this research.
( i ) To understand the complicated behavior of high dimensional chaos, we began studies invariant manifolds and On-off intermittency around them, already. We developed this study. Then we found that the complex behavior of the large degree of freedom chaos (chaotic itinerancy) is wondering motion between invariant manifolds and shown that we get clear characterization by statistical coarse-graining,
( ii ) The properties of On-off intermittency that is the base of ( i ) had been argued with perturbation theory. We got new knowledge by treating them by non-preservative methods.
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( iii ) Many non-chaotic attractors (fixed points, periodic orbits, and quasi-periodic orbits) can exist in a large degree of freedom (the number of attractor suddenly increases with increase of system size). We studied the properties from a viewpoint of response for noise in particular and was found that enough small noise tied attractor and caused intermittent phenomena. In addition, we found what we could describe the motion as anomalous diffusion in macro-quantities of system.
( iv ) We studied also relation intermittency of chaos in conservative dynamical systems and low dimensional invariant structure.
Next to a study about the behavior of dynamical systems mentioned above, we can develop approach for more complicated behavior. We started (a) a characterization of complicated behavior in generalized shift maps by anomalous diffusion, (b) an analysis of EEG pattern by time-series' entropy, (c) an analysis of intermittency of explosions of SAKURAJIMA volcano and (d) a study for the complicated behavior of dynamical systems with the hierarchical structure which seemed to have invariant manifold in an invariant manifold. Less
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