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2001 Fiscal Year Final Research Report Summary

All inclusive synchronization phenomena-based studies on transmissions of energies and information in coupled systems of electric circuits

Research Project

Project/Area Number 12834006
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research InstitutionFUTURE UNIVERSITY-HAKODATE

Principal Investigator

UEDA Yoshisuke  FUTURE UNIVERSITY-HAKODATE, PROFESSOR, システム情報科学部, 教授 (00025959)

Co-Investigator(Kenkyū-buntansha) OKUMURA Kohshi  KYOTO UNIVERSITY, PROFESSOR, 大学院・工学研究科, 教授 (50026241)
VOLODYMYR Riabov  FUTURE UNIVERSITY-HAKODATE, ASSOCIATE PROFESSOR, システム情報科学部, 助教授 (10325904)
TAKAYASU Misako  FUTURE UNIVERSITY-HAKODATE, ASSOCIATE PROFESSOR, システム情報科学部, 助教授 (20296776)
KURAMITSU Masami  KYOTO UNIVERSITY, LECTURER, 大学院・工学研究科, 講師 (40026084)
HIKIHARA Takashi  KYOTO UNIVERSITY, PROFESSOR, 大学院・工学研究科, 教授 (70198985)
Project Period (FY) 2000 – 2001
KeywordsSynchronization / Bifurcation / Chaos / Broken-Egg Chaotic Attractor / Chaotic Sea / Spatio-Temporal Chaos / Magneto-Elastic Beam / Quasi-Periodic Wave
Research Abstract

In this study we have clarified synchronizing phenomena in the wide sense, which include quasi-periodic and chaotic synchronizations in various nonlinear systems.
First, we returned to the context of nonlinear oscillation theory in which we began, in 1961, our experience with chaotic behavior. This context involves the systems of forced self-oscillators arising in electronic circuits. We combined earlier examples into a simple mixed system, and obtained information on the bifurcation diagram of this system. In particular, the parameter regime of the broken-egg chaotic attractor is mapped.
Next, on behalf of the analysis on quasi-periodic oscillation and chaotic behavior in coupled electric system, a coupled magneto-elastic beam system, which has elastically continuous and magnetically discrete characteristics, was proposed. It made us possible to examine the physical phenomenon experimentally and to obtain the appropriate mathematical model. The results obtained by one of members showed the followings :
1) The long wave length phenomena cannot be found in the finite dimensional system. Therefore, the partial differential equation is not physically appropriate to describe the short wave length phenomena.
2) The dynamical behavior in the finite element nonlinear coupled systems, which imply between partial differential equations and ordinary differential equations, can be described by difference-differential equations qualitatively based on the experimental results on the synchronous phenomenon and the wave propagation.
3) The unstable standing wave has an important role to realize the onset of wave propagation. The high dimensional heteroclinic structure of manifolds is substantial for the onset. These results give us the great knowledge on the relation between the phenomena in physical models and in the mathematical models.

  • Research Products

    (13 results)

All Other

All Publications (13 results)

  • [Publications] Tetsuro Endo: "Explosion of strange attractors and crisis-induced intermittency from a forced phase-locked loopcircuit : Theory and experiments"International Journal of Bifurcation and Chaos. 10・4. 891-912 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hidetaka Ito: "Emergence of a multidomain regime and spatiotemporal chaos in Gunn diodes under impact ionization conditions"Physics Letters A. 281・3. 312-317 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi Hikihara: "Quasi-periodic wave and its bifurcation in coupled magneto-elastic beam system"Physics Letters A. 281・3. 155-160 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi Hikihara: "Wave and basin structure in spatially coupled magneto-elastic beam system -Transitions between coexisting wave solutions"International Journal of Bifurcation and Chaos. 11・4. 999-1018 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hidetaka Ito: "Chaotic multidomain oscillations in a spatially-extended semiconductor device"IEICE Trans.Fundamentals. E84-A. 2908-2914 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hirofumi Ohta: "Unstable limit cycles in an electric power system and basin boundary of voltage collapse"Chaos Solitons and Fractals. 12・12. 159-172 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Yoshisuke Ueda: "The Road to Chaos-II"Aerial Press, Inc.POB 1360, Santa Cruz, CA 95061 ISBN 0-942344-23-5. 255 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hirofumi Ohta and Yoshisuke Ueda: "Unstable limit cycles in an electric power system and basin boundary of voltage collapse"Chaos Solitons and Fractals. 12.12. 159-172 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi Hikihara, Kentaro Torii and Yoshisuke Ueda: "Wave and basin structure in spatially coupled magneto-elastic beam system-Transitions between coexisting wave solutions"International Journal of Bifurcation and Chaos. 11.4. 999-1018 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi Hikihara, Kentaro Torii and Yoshisuke Ueda: "Quasi-periodic wave and its bifurcation in coupled magneto-elastic beam system"Physics Letters A. 281・3. 155-160 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hidetaka Ito and Yoshisuke Ueda: "Emergence of a multidomain regime and spatiotemporal chaos in Gunn diodes under impact ionization conditions"Physics Letters A. 281・3. 312-317 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tetsuro Endo, Wataru Ohno and Yoshisuke Ueda: "Explosion of strange attractors and crisis-induced intermittency from a forced phase-locked loopcircuit: Theory and experiments"International Journal of Bifurcation and Chaos. 10.4. 891-912 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoshisuke Ueda: "Reflections on the broken-eggchaoticattractor, in The Road to Chaos II (Monograph)"Aerial Press, Inc. POB 1360, Santa Cruz, CA 95061, ISBN 0-942344-23-5. 229-243 (2001)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2003-09-17   Modified: 2021-04-07  

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