Theory for the mathematical modeling of complicated systems

• Project/Area Number: 26310212
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 特設分野
• Research Field: Mathematical Sciences in Search of New Cooperation
• Research Institution: Hokkaido University
• Principal Investigator: EI Shin-Ichiro 北海道大学, 理学研究院, 教授 (30201362)
• Project Period (FY): 2014-07-18 – 2019-03-31
• Project Status: Completed (Fiscal Year 2018)
• Budget Amount: ¥11,830,000 (Direct Cost: ¥9,100,000、Indirect Cost: ¥2,730,000); Fiscal Year 2018: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2017: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2016: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2015: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000); Fiscal Year 2014: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
• Keywords: スポット解 / 相互作用 / 中心多様体 / 非局所効果 / 細胞極性 / 積分核 / 代謝ネットワーク / 普遍構造 / 局在解 / 曲面上の運動 / モデル化 / 自己組織化 / 反応拡散モデル / 樟脳片 / 数理モデル / 分岐構造

Outline of Final Research Achievements

The motion of spot-like localized solutions was successfully derived by combining weak interaction and bifurcation approaches for multi-variable reaction-diffusion systems. The results were applied to the analysis of the interaction between two camphor tips with elliptic shapes and the theoretically reduced motion was checked in real experiments. The results were also applied to the motion of spot solution on a curved surface and the motion depending on the gradient of Gaussian curvature of the surface was derived.

Academic Significance and Societal Importance of the Research Achievements

現象を数理モデルによりある程度忠実に記述する際, 多数の未知変数が必要となったり, 非線形項などをきちんと決めることができないといった状況が生じる．そのような場合でも, 分岐構造や相互作用といった, 実験により容易に検証可能な条件のみで理論的に帰結できる普遍的な解の性質を導いたことは, モデルの検証として役立つと同時に, 解の本質的構造の理解につながると期待される．

Research Products

• [Int'l Joint Research] Ting Hua University/Taiwan University(その他の国・地域 台湾)
• [Int'l Joint Research] NCTS/National Tsing Hua University(台湾)
• [Int'l Joint Research] Math. Dept./Capital Normal University(China)
• [Int'l Joint Research] National Tsing Hua University(Taiwan)
• [Int'l Joint Research] Queensland University of Technology(オーストラリア)
• [Journal Article] Heterogeneity-induced effects for pulse dynamics in FitzHugh-Nagumo type systems (2018)
  • Author(s): Chen Chao-Nien、Ei Shin-Ichiro、Tzeng Shyuh-yaur
  • Journal Title: Physica D: Nonlinear Phenomena Volume: 382-383 Pages: 22-32
  • DOI: 10.1016/j.physd.2018.07.001
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Dynamics of Localized Unimodal Patterns in Reaction-Diffusion Systems for Cell Polarization by Extracellular Signaling (2018)
  • Author(s): Kuwamura Masataka、Seirin-Lee Sungrim、Ei Shin-ichiro
  • Journal Title: SIAM Journal on Applied Mathematics Volume: 78 Issue: 6 Pages: 3238-3257
  • DOI: 10.1137/18m1163749
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] JAK/STAT guarantees robust neural stem cell differentiation by shutting off biological noise (2018)
  • Author(s): Tanaka, Y., Yasugi, T.,Nagayama, M., Sato, M. and Shin-Ichiro Ei
  • Journal Title: Scientific Reports Volume: 8 Pages: 12484-12484
  • NAID: 120006536943
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Jak/stat guarantees robust differentiation of neural stem cells by shutting off biological noises in the developing fly brain (2018)
  • Author(s): M Sato, T Yasugi, Y Tanaka, M Nagayama, S. Ei
  • Journal Title: Cytokine Volume: 100 Pages: 13-29
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] 微分方程式を導出する-常微分方程式 (2018)
  • Author(s): 栄 伸一郎
  • Journal Title: 数理科学 Volume: 11 Pages: 7-13
• [Journal Article] Interaction of non-radially symmetric camphor particles, (2017)
  • Author(s): Shin-Ichiro Ei, Hiroyuki Kitahata, Yuki Koyano, Masaharu Nagayama
  • Journal Title: Physica D Volume: 366 Pages: 10-26
  • DOI: 10.1016/j.physd.2017.11.004
  • NAID: 120006769933
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Mathematical Modeling for Meshwork Formation of Endothelial Cells in Fibrin Gels (2017)
  • Author(s): Daiki Sasaki, Hitomi Nakajima, Yoshimi Yamaguchi, Ryuji Yokokawa, Shin-Ichiro Ei, Takashi Miura
  • Journal Title: Journal of Theoretical Biology Volume: 429 Pages: 95-104
  • DOI: 10.1016/j.jtbi.2017.06.012
  • Peer Reviewed / Open Access
• [Journal Article] 反応拡散型数理モデル -分岐構造を通した数理モデルに対する一考察- (2017)
  • Author(s): 栄 伸一郎
  • Journal Title: 実験医学増刊号, 羊土社 Volume: 35 Pages: 60-67
• [Journal Article] 反応拡散型数理モデル -分岐構造を通した数理モデルに対する一考察 (2017)
  • Author(s): 栄 伸一郎
  • Journal Title: 実験医学増刊号, 羊土社 Volume: 35 Pages: 60-67
  • Peer Reviewed
• [Journal Article] Instability of multi-spot patterns in shadow systems of reaction-diffusion equations (2015)
  • Author(s): Yanagida, Eiji; Ikeda, Kota; Ei, Shin-Ichiro
  • Journal Title: Commun. Pure Appl. Anal. Volume: 14 Pages: 717-736
  • NAID: 120005732975
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] REDUCED MODEL FROM A REACTION-DIFFUSION SYSTEM OF COLLECTIVE MOTION OF CAMPHOR BOATS (2015)
  • Author(s): S.-I. Ei, K. Ikeda, M. Nagayama and A. Tomoeda
  • Journal Title: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS SERIES S Volume: 8 Issue: 5 Pages: 847-856
  • DOI: 10.3934/dcdss.2015.8.847
  • NAID: 120005853055
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Annihilation of two interfaces in a hybrid system (2015)
  • Author(s): Shin-Ichiro Ei, Kei Nishi, Yasumasa Nishiura, Takashi Teramoto
  • Journal Title: American Institute of Mathematical Sciences Volume: 8 Issue: 5 Pages: 857-869
  • DOI: 10.3934/dcdss.2015.8.857
  • NAID: 120005649132
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] 時・空間パターンの数理解析 (2015)
  • Author(s): 栄 伸一郎
  • Journal Title: 電子情報通信学会誌 Volume: 98 Pages: 961-966
  • Peer Reviewed
• [Journal Article] 曲面上におけるパターンの運動 (2015)
  • Author(s): 栄 伸一郎
  • Journal Title: 植物科学最前線 BSJ-Review Volume: 2015
  • Peer Reviewed
• [Journal Article] Instability of multi-spot patterns in shadow systems of reaction-diffusion equations (2015)
  • Author(s): Yanagida, Eiji; Ikeda, Kota; Ei, Shin-Ichiro
  • Journal Title: Commun. Pure Appl. Anal. Volume: 14 Pages: 717-736
  • NAID: 120005732975
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] APPLICATION OF A CENTER MANIFOLD THEORY TO A REACTION-DIFFUSION SYSTEM OF COLLECTIVE MOTION OF CAMPHOR DISKS AND BOATS (2014)
  • Author(s): S.-I. Ei, K. Ikeda, M. Nagayama and A. Tomoeda
  • Journal Title: MATHEMATICA BOHEMICA Volume: 139 Pages: 363-371
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] ２次元領域におけるスポット解の運動について (2014)
  • Author(s): 栄 伸一郎
  • Journal Title: フォーラム, 応用数理 Volume: 24 Pages: 34-36
  • Peer Reviewed
• [Presentation] Interaction of non-radially symmetric camphor particles (2019)
  • Author(s): 栄 伸一郎
  • Organizer: PDE seminar in Ting Hua University
  • Int'l Joint Research / Invited
• [Presentation] Motion of a pulse for mass-conserved reaction-diffusion systems (2019)
  • Author(s): 栄 伸一郎
  • Organizer: 反応拡散方程式と非線形分散型方程式の解の挙動 RIMS共同研究
  • Invited
• [Presentation] 分化の波を通して見る数理モデル構築と解析のための新しい試み (2019)
  • Author(s): 栄 伸一郎
  • Organizer: CREST・さきがけ数学関連領域合同シンポジウム 「数学パワーが世界を変える 2019」
  • Invited
• [Presentation] 反応拡散系におけるスローダイナミクスの導出 (2018)
  • Author(s): 栄 伸一郎
  • Organizer: 研究会 「くりこみ群によるスケールの分離とスローダイナミクス」
  • Invited
• [Presentation] Interaction of pulses for mass-conserved reaction-diffusion systems related to cell polarity (2018)
  • Author(s): 栄 伸一郎
  • Organizer: 2018 China-Japan Workshop on Nonlinear Diffusion Problems
  • Int'l Joint Research / Invited
• [Presentation] Motion of pulse solution to a reaction-diffusion system with conservation of mass (2017)
  • Author(s): Ei, Shin-Ichiro
  • Organizer: Mathematical Analysis on Nonlinear PDEs
  • Place of Presentation: Tohoku University, Sendai, Miyagi
  • Year and Date: 2017-01-06
  • Int'l Joint Research / Invited
• [Presentation] Motion of a Pulse for Mass-conserved Reaction-diffusion Systems Related to Cell Polarity (2017)
  • Author(s): S.-I. EI
  • Organizer: MIMS The International Conference on “Reaction-diffusion system, theory and applications”
  • Int'l Joint Research / Invited
• [Presentation] The motion of a spot in two dimensional bounded domain (2017)
  • Author(s): S.-I. Ei
  • Organizer: PDE seminar in Capital Normal University, Beijing
  • Int'l Joint Research / Invited
• [Presentation] 質量保存則を伴う反応拡散モデルにおけるパルスの運動について (2017)
  • Author(s): 栄 伸一郎
  • Organizer: 函館応用数理解析セミナー
  • Invited
• [Presentation] Multi-peak localized solutions for reaction-diffusion systems on two dimensional curved surface (2016)
  • Author(s): Ei, Shin-Ichiro
  • Organizer: The Second Workshop on Differential Geometry and Differential equations
  • Place of Presentation: Renmin University of China, Bajing, China
  • Year and Date: 2016-11-12
  • Int'l Joint Research / Invited
• [Presentation] Effect of boundaries on the motion of a spot solution in a two dimensional domain (2016)
  • Author(s): Ei, Shin-Ichiro
  • Organizer: Reaction-Diffusion Systems in Mathematics and Biomedecine
  • Place of Presentation: Villa Clythia, Frejus, France
  • Year and Date: 2016-09-19
  • Int'l Joint Research / Invited
• [Presentation] Pulse interaction in modified FitzHugh-Nagumo equations (2016)
  • Author(s): Ei, Shin-Ichiro
  • Organizer: Mathematics of Pattern Formation
  • Place of Presentation: Mathematical Research and Conference Center in Bedlewo, Poland
  • Year and Date: 2016-09-12
  • Int'l Joint Research / Invited
• [Presentation] Effect of boundaries on the motion of a spot solution in a two dimensional domain (2016)
  • Author(s): Ei, Shin-Ichiro
  • Organizer: Joint Australia-Japan workshop on dynamical systems with applications in life sciences
  • Place of Presentation: Queensland University of Technology, Brisbane, Queensland, Australia
  • Year and Date: 2016-07-18
  • Int'l Joint Research / Invited
• [Presentation] Pulse dynamics of modified FitzHugh-Nagumo equation (2016)
  • Author(s): 栄 伸一郎
  • Organizer: 仙台応用数学研究集会
  • Place of Presentation: 東北大学 (宮城県・仙台市)
  • Year and Date: 2016-03-09
  • Int'l Joint Research / Invited
• [Presentation] Pulse dynamics of modified FitzHugh-Nagumo equation (2015)
  • Author(s): 栄 伸一郎
  • Organizer: 2015 NCTS Workshop on Partial Differential Equations and Applied Mathematics
  • Place of Presentation: 新竹市(台湾)
  • Year and Date: 2015-12-29
  • Int'l Joint Research / Invited
• [Presentation] Shape-dependent motion of interacting camphor (2015)
  • Author(s): 栄 伸一郎
  • Organizer: 16th RIES-Hokudai International Symposium
  • Place of Presentation: Chateraise Gateaux Kingdom (北海道・札幌市)
  • Year and Date: 2015-11-10
  • Int'l Joint Research / Invited
• [Presentation] Shape-dependent motion of interacting camphors (2015)
  • Author(s): 栄 伸一郎
  • Organizer: 第5回室蘭非線形解析研究会
  • Place of Presentation: 室蘭工業大学 (北海道・室蘭市)
  • Year and Date: 2015-11-06
  • Int'l Joint Research / Invited
• [Presentation] 不安定化がパターンを生む (2015)
  • Author(s): 栄 伸一郎
  • Organizer: 鉄鋼インフオマティクス研究会第6回研究会プログラム
  • Place of Presentation: 九州大学 (福岡県・福岡市)
  • Year and Date: 2015-09-01
  • Invited
• [Presentation] Motion of interacting camphors (2015)
  • Author(s): 栄 伸一郎
  • Organizer: 第1 6 回北東数学解析研究会
  • Place of Presentation: 東北大学, 仙台市
  • Year and Date: 2015-02-15 – 2015-02-16
  • Invited
• [Presentation] Motion of interacting camphors (2014)
  • Author(s): 栄 伸一郎
  • Organizer: 2014 NCTS Applied Math. & PDE Seminar
  • Place of Presentation: 国立精華大学, 新竹市, 台湾
  • Year and Date: 2014-12-02
  • Invited
• [Presentation] Motion of patterns on a curved surface (2014)
  • Author(s): 栄 伸一郎
  • Organizer: 日本植物学会第78回大会
  • Place of Presentation: 明治大学生田キャンパス, 川崎市
  • Year and Date: 2014-09-12 – 2014-09-14
  • Invited
• [Presentation] 化学反応系に現れるスパイラル波への数学的アプローチについて (2014)
  • Author(s): 栄 伸一郎
  • Organizer: 渦の特徴付け研究集会
  • Place of Presentation: 北海道大学, 札幌市
  • Year and Date: 2014-07-28 – 2014-07-30
  • Invited
• [Presentation] Pulse dynamics in FitzHugh-Nagumosystems on heterogeneous media (2014)
  • Author(s): 栄 伸一郎
  • Organizer: mini-workshop on Modeling, Simulation & Analysis of Pattern Formation
  • Place of Presentation: 東北大学, 仙台市
  • Year and Date: 2014-07-26 – 2014-07-27
  • Invited
• [Remarks] CREST
  • URL: http://www.math.sci.hokudai.ac.jp/crest_rd/
• [Remarks] Ei-Lab
  • URL: http://www.math.sci.hokudai.ac.jp/~Eichiro/
• [Funded Workshop] Second Joint Australia-Japan workshop on dynamical systems with applications in life science (2018)
• [Funded Workshop] Patterns and dynamics with nonlocal effect (2017)
• [Funded Workshop] New mathematical approaches for understanding of biological phenomena (2017)
• [Funded Workshop] Pattern formation problems with non-local effects (2017)
• [Funded Workshop] 第41回偏微分方程式論札幌シンポジウム (2016)
  • Place of Presentation: 北海道大学, 北海道札幌市
  • Year and Date: 2016-08-08
• [Funded Workshop] ソウル大ジョイントシンポジウム分科会 (Mathematical analysis andapplications) (2015)
  • Place of Presentation: ソウル大学 (韓国・ソウル市)
  • Year and Date: 2015-11-27