非線形方程式の縮約による新しい数理構造の探求 : 減衰モード・ノイズ・振動結合の非自明な効果  [in Japanese] Reduction Methods Shed Light on Novel Mathematical Structures : Non-trivial Effects of Damping Modes, Noise, and Oscillatory Coupling  [in Japanese]

Abstract

一見逆説的で予想外な現象の発見は,研究の大きな醍醐味の一つです.その現象が単純な機構で生じ,また,普遍的であれば,なおさら重要でしょう.中心多様体縮約,位相縮約を用いてのこのような現象の探求について,三つ紹介させて頂きます.縮約は,例えて言うなら,方程式の'相転移点'から普遍的な数理模型を導出する物理・数学手法です.本稿では,三つの研究を各々独立に述べますが,「縮約による新しい数理構造の探求」という一貫したテーマに基づき,実際,相互に関わり深く発展させてきたものです.

Three subjects are presented. 1: Marginally stable long-wavelength modes, due to spontaneous symmetry breaking or conservation law, can cause an initially uniform state to evolve into a spatiotemporal chaos instead of spatially periodic structure. 2: Independent limit cycle oscillators can be synchronized by weak, common additive noise regardless of their detailed oscillatory dynamics and initial phase distributions. 3: Assemblies of dynamical elements can exhibit a rich variety of patterns due to the fact that the interaction between elements can be attractive or repulsive, depending on internal states of the elements.

Journal

Butsuri   [List of Volumes]

Butsuri 63(12), 945-952, 2008-12-05  [Table of Contents]

The Physical Society of Japan (JPS)

References:  3

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Codes

  • NII Article ID (NAID) :
    110007007549
  • NII NACSIS-CAT ID (NCID) :
    AN00196952
  • Text Lang :
    JPN
  • Article Type :
    REV
  • ISSN :
    00290181
  • NDL Article ID :
    9723677
  • NDL Source Classification :
    ZM35(科学技術--物理学)
  • NDL Call No. :
    Z15-13
  • Databases :
    CJP  NDL  NII-ELS 

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