| Project/Area Number |
62540280
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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 |
物理学一般
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| Research Institution | Kyoto University |
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Principal Investigator |
YOSHIKI KURAMOTO Professor, Department of Physics, Kyoto University, 理学部, 教授 (40037247)
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| Co-Investigator(Kenkyū-buntansha) |
SHIGERU SHINOMOTO Assistant, Department of Physics, Kyoto University, 理学部, 助手 (60187383)
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| Project Period (FY) |
1987 – 1988
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| Project Status |
Completed (Fiscal Year 1988)
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| Budget Amount *help |
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1988: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1987: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | dissipative dynamical systems with many degrees of freedom / dynamical contraction / entrainment / phasedynamics / rotator model / 神経回路網 / 秩序パラメター / 振動子集団 / 位相乱流 / 実効発展方程式 / 乱流ゆらぎ / くり込まれた輸送係数 |
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| Research Abstract |
The goal of the present research project is to develop a theory of dynamical contraction aplicable to nonlinear dissipative systems with infinitely many degrees of freedom. This was achieved in the following two directions:
(1) Here the interest is in how it is possible to solve ordinary statistical mechanical problems (equilibrium and non-equilibrium) for non-hamiltonian systems without known invariant measure. As a prototypal system for which this is actually possible, a population of coupled limit-cycle oscillators with mean-field coupling was considered, where the oscillators were modelled by active rotators. Near the onset of collective oscillation, we succeeded in deliving an evolution equation for a suitably defined order parameter in a closed form. Then it was generated into a langevin type equation, which made it possible to study critical fluctuations. A crucial point is that the present system can be approximated by virtue of the mean field coupling by and ergodic dynamical s
… More
ystem on a high-dimensional torus, even though it is in principle a chaotic dynamical system with singular invariant measure. This property provides an approximate invariant measure, and hence "local equilibrium distribution" with given value of the order parameter is well defined.
(2) A universal structure in the existing contraction theories for systems of partial differential equations was extracted, and the phasedynamics theory was formulated in an unambiguous manner. The importance of the phasedynamics has recently been realized in connection with pattern dynamics and weak turbulence in spatially general viewpoint. Strong structural similarities underlying a number of representative theories of dynamical contraction developed in the past were also made clear. Other than the sujects described above, we have made a considerable progress in the contraction of the phase turbulence equation (KS eqn.), which was one of the main subjects of our initial research program, although the results have not been published yet. Finally, some research works on information processing in model neural networks were made by a member of the present project team. Less
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