数理解析研究紹介教員紹介柳田　達雄
教授　柳田　達雄

研究分野

非線形数理科学，時空カオス，パターン形成

研究内容

　熱平衡から遠く外れた非平衡開放系で見られる散逸構造や時空カオス現象に興味がある．特に自然界に見られる時間と共に変動するパターンや散逸構造の生成機構の解明を目指している．具体的には，河川・雲・沸騰などの従来は解析が困難とされてきた自己組織された複雑なシステムをセルオートマトン，結合格子写像，微分方程式により数理モデル化し，シミュレーションと力学系や分岐・カオス理論を用い動的な時空パターンの数理的解析を行っている．また，による力学モデルの解構造及び分岐構造のマルコフ連鎖モンテカルロ法による解析．また，ネットワーク結合した力学素子が与えられた機能を満たすようにモデルをデザインし生態・遺伝子・生体などへの応用を目指している．
　
　
　
　
　

 反応拡散系のスパイラル・カオス
反応拡散系のスパイラル・カオス

羽ばたき飛行の数理モデル
羽ばたき飛行の数理モデル

雲のパターン形成の数理モデル
雲のパターン形成の数理モデル

キーワード

カオス，ニューロン・モデル，パターン形成，時空カオス，構成論的モデル化，混相流体，粉粒体，結合格子写像，ハミルトン系，位相振動子，ネットワークダイナミクス

個人のWebSite

学術論文

  1. Tetsuro Konishi and Tatsuo Yanagita, “Slow relaxation to equipartition in spring-chain systems”, Journal of Statistical Mechanics, p. P09001- P09015 (2010)
  2. Tatsuo Yanagita and Alexander S. Mikhailov, “Design of easily synchronizable oscillator networks using Monte Carlo Optimization method”, Physical Review E, 81,056204 (2010)
  3. Tatsuo Yanagita and Tamotsu Onozaki, “Dynamics of Market Structure Driven by the Degree of Consumer's Rationality”, Physica A, vol. 389, p.1041-1054 (2010)
  4. Tetsuro Konishi and Tatsuo Yanagita, “Energetic motion of end-particles in constrained dynamical systems”, Journal of Statistical Mechanics, p. L09001-L09010 (2009)
  5. Tatsuo Yanagita and Yukito Iba, “Exploration of Order in Chaos using the Replica Exchange Monte Carlo method”, Journal of Statistical Mechanics, Journal of Statistical Mechanics, p. P02043-P02058 (2009)
  6. Tatsuo Yanagita, Hiromichi Suetani and Kazuyuki Aihara, “Bifurcation analysis of solitary pulse, synchronized pulses and reentrant waves in laterally coupled excitable fibers”, Physical Review E, 78, p. 05628-056039 (2008), [Selected for Virtual Journal of Biological Physics Research, Vol. 16-10 (2008)]
  7. Hiromichi Suetani, Tatsuo Yanagita and Kazuyuki Aihara, “Pulse Dynamics in Coupled Excitable Fibers: Soliton-like Collision, Recombination, and Overtaking”, International Journal of Bifurcations and Chaos, 18, p. 2289-2308(2008)
  8. Tatsuo Yanagita and Tamotsu Onozaki, “Dynamics of a Market with Heterogeneous Learning Agents”, Journal of Economic Interaction and Coordination, 3,p.107-118 (2008)
  9. Tatsuo Yanagita and Tamotsu Onozaki, “A Model of Market Structure Dynamics with Boundedly Rational of a Agents”, Agent-Based Approaches in Economics and Social Complex System V, p.255-266 (2008)
  10. Tatsuo Yanagita, “Input-output relation of FitzHugh-Nagumo elements arranged in a trifurcated structure”, Physical Review E. 76,56215-56228(2007)
  11. T. Onozaki, Tatsuo Yanagita, T. Kaizoji and K. Toyabe : “Regional Business Cycle Synchronization through Expectations”, Physica A, 383,102-107(2007)
  12. Yoshihito Oyama, Tatsuo Yanagita and Takashi Ichinomiya, “Numerical Analysis of FitzHugh-Nagumo neurons on random networks”, Progress of Theoretical Physics, 161, 389-392 (2006)
  13. Tatsuo Yanagita, Yasumasa Nishiura and Ryo Kobayashi, “Resonance and the formation of death-spot in one-dimensional FitzHugh-Nagumo equations”, Progress of Theoretical Physics, 161, 393-396 (2006)
  14. Makoto Iima and Tatsuo Yanagita, “A transition from ascending flight to vertical hovering: A study of a symmetric flapping model”, Europhysics Letter, 74,p.55-61 (2006)
  15. Makoto Iima and Tatsuo Yanagita, “Asymmetric Motion of a Two-Dimensional Symmetric Flapping Model”, Fluid Dynamics Research, 36, p. 407-425 (2005)
  16. Tatsuo Yanagita, Yasumasa Nishiura and Ryo Kobayashi, “Signal propagation and failure in one-dimensional FitzHugh-Nagumo equations with periodic stimuli”, Physical Review E, 71, p36226-36230　(2005)
  17. Yasumasa Nishiura, Daishin Ueyama and Tatsuo Yanagita, “Chaotic Pulses for Discrete Reaction Diffusion Systems”, SIAM Journal of Applied Dynamical Systems, 4, p.733-754 (2005)
  18. Tatsuo Yanagita, Takashi Ichinomiya and Yoshihito Oyama, “A pair of excitable FitzHugh-Nagumo elements: Synchronization, Multistability and Chaos”, Physical Review E, 72, p56218-56224 (2005)
  19. Tamotsu Onozaki and Tatsuo Yanagita, “Monopoly, Oligopoly and Invisible Hand”, Chaos, Solitons & Fractals, 18, p.537-547 (2003)
  20. Makoto Iima and Tatsuo Yanagita,”Is a 2D Butterfly able to fly by Symmetrical Flapping?”, Journal of Phys. Soc. Japan, 70,p5-8(2001)
  21. 西浦廉政, 上山大信，柳田達雄,”離散散逸系におけるカオス的パルス”,応用数理，vol.11-2, p.25-39(2001)
  22. Makoto Iima and Tatsuo Yanagita, "An Analysis of a Symmetric Flapping Model: A Symmetry-Breaking Mechanism and Its Universality", Theoretical and Applied Mechanics, 50, p.237-245(2001)
  23. Tatsuo Yanagita,”A Three-Dimensional Cellular Automaton Model of Segregation of Granular Materials in a Rotating Cylinder”, Physical Review Letters, 82:3488-3491(1999)
  24. Tatsuo Yanagita and Kunihiko Kaneko, Modeling and Characterization of Cloud Dynamics”, Physical Review Letters, 78:4297-4301(1997)