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KUWAMURA Masataka
Graduate School of Human Development and Environment / Department of Human Environmental Science
Professor

Researcher basic information

■ Research Keyword
  • nonlinear phenomenon
  • differential equation
■ Research Areas
  • Natural sciences / Applied mathematics and statistics
  • Natural sciences / Basic mathematics

Research activity information

■ Paper
  • Hideo Ikeda, Masataka Kuwamura
    Elsevier BV, 2025, Journal of Differential Equations, 440, 113430
    [Refereed]
    Scientific journal

  • Single Transition Layer in Mass-Conserving Reaction-Diffusion Systems with Bistable Nonlinearity
    Masataka Kuwamura, Takashi Teramoto, Hideo Ikeda
    2024, Nonlinearity, 37, 115013, English
    [Refereed]
    Scientific journal
    Link to Kobe Univ. Repository (Kernel)

  • Masataka Kuwamura, Hirofumi Izuhara, Shin-ichiro Ei
    Springer Science and Business Media LLC, 2022, Journal of Mathematical Biology, 84(4) (4), 22, English
    [Refereed]
    Scientific journal
    Link to Kobe Univ. Repository (Kernel)

  • Dynamics of localized unimodal patterns in reaction-diffusion systems for cell polarization by extracellular signaling
    KUWAMURA MASATAKA, SUNGRIM SEIRIN-LEE, EI SHIN-ICHIRO
    2018, SIAM Journal on Applied Mathematics, 78(6) (6), 3238 - 3257, English
    [Refereed]
    Scientific journal
    Link to Kobe Univ. Repository (Kernel)

  • Masataka Kuwamura, Hirofumi Izuhara
    2017, CHAOS, 27(3) (3), 012908, English
    [Refereed]
    Scientific journal
    Link to Kobe Univ. Repository (Kernel)

  • Turing instabilities in prey-predator systems with dormancy of predators
    Masataka Kuwamura
    2015, Journal of Mathematical Biology, 71, 125 - 149, English
    [Refereed]
    Scientific journal

  • Perturbations and dynamics of reaction-diffusion systems with mass conservation
    KUWAMURA MASATAKA, Yoshihisa Morita
    2015, Physical Review E, 92, 012908, English
    [Refereed]
    Scientific journal
    Link to Kobe Univ. Repository (Kernel)

  • Stability of coexisting equilibrium of prey-predator systems with dormancy of predators
    Masataka Kuwamura
    2014, Funkcialaj ekvacioj. Serio internacia, 57(2) (2), 339 - 350, English
    [Refereed]
    Scientific journal

  • Masataka Kuwamura, Kousuke Maeda, Takashi Adachi-Yamada
    2012, Journal of Biological Dynamics, 6(2) (2), 267 - 276, English
    [Refereed]
    Scientific journal

  • Takefumi Nakazawa, Masataka Kuwamura, Norio Yamamura
    2011, Population Ecology, 53(2) (2), 341 - 350, English
    [Refereed]
    Scientific journal

  • Masataka Kuwamura, Takefumi Nakazawa
    2011, SIAM Journal on Applied Mathematics, 71(1) (1), 169 - 179, English
    [Refereed]
    Scientific journal

  • Masataka Kuwamura, Kousuke Maeda, Takashi Adachi-Yamada
    Informa UK Limited, 2010, Journal of Biological Dynamics, 4(3) (3), 248 - 257
    [Refereed]
    Scientific journal

  • Mixed-mode oscillations and chaos in a prey-predator system with dormancy of predators
    Masataka Kuwamura, Hayato Chiba
    2009, CHAOS, 19, 043121, English
    [Refereed]
    Scientific journal

  • Masataka Kuwamura, Takefumi Nakazawa, Toshiyuki Ogawa
    2009, Journal of Mathematical Biology, 58(3) (3), 459 - 479, English
    [Refereed]
    Scientific journal

  • Deviation from the predicted wavenumber in a mode selection problem for the Turing patterns
    Masataka Kuwamura
    2008, Japan Journal of Industrial and Applied Mathematics, 25, 281 - 303, English
    [Refereed]
    Scientific journal

  • The Hamiltonian formalism in reaction-diffusion systems
    Masataka Kuwamura
    2007, Advanced Studies in Pure Mathematics, 47, 635 - 646, English
    [Refereed]
    Scientific journal

  • Krein's formula for indefinite multipliers in linear periodic Hamiltonian systems
    Masataka Kuwamura, Eiji Yanagida
    2006, Journal of Differential Equations, 230, 446 - 464, English
    [Refereed]
    Scientific journal

  • M Kuwamura
    2005, SIAM Journal on Applied Mathematics, 65(2) (2), 618 - 643, English
    [Refereed]
    Scientific journal

  • A variational approach to singular perturbation problems in reaction-diffusion systems
    Shin-ichiro Ei, Masataka Kuwamura, Yoshihisa Morita
    2005, Physica D, 207, 171 - 219, English
    [Refereed]
    Scientific journal

  • The Eckhaus and zigzag instability criteria in gradient/skew-gradient dissipative systems
    M Kuwamura, E Yanagida
    2003, Physica D, 175, 185 - 195, English
    [Refereed]
    Scientific journal

  • A perspective of renormalization group approaches
    Masataka Kuwamura
    2001, Japan Journal of Industrial and Applied Mathematics, 187, 739 - 768, English
    [Refereed]
    Scientific journal

  • The stability of roll solutions of the two-dimensional Swift-Hohenberg equation and the phase-diffusion equation
    M Kuwamura
    1996, SIAM Journal on Mathematical Analysis, 27(5) (5), 1311 - 1335, English
    [Refereed]
    Scientific journal

  • Phase dynamics method with applications to the Swift-Hohenberg equation
    Masataka Kuwamura
    1994, Journal of Dynamics and Differential Equations, 6, 185 - 225, English
    [Refereed]
    Scientific journal

  • Very slow dynamics for some reaction-diffusion system with activator-inhibitor type
    Masataka Kuwamura, Shin-ichiro Ei, Masayasu Mimura
    1992, Japan Journal of Industrial and Applied Mathematics, 9, 35 - 77, English
    [Refereed]
    Scientific journal

■ Books And Other Publications
  • 応用解析概論
    KUWAMURA MASATAKA
    Single work, 裳華房, Nov. 2018, Japanese
    Textbook

  • 線形代数学入門
    KUWAMURA MASATAKA
    Single work, 裳華房, Feb. 2016, Japanese
    Textbook

  • パターン形成と分岐理論
    KUWAMURA MASATAKA
    Single work, 共立出版, Jan. 2015, Japanese
    Scholarly book

  • 微分積分入門
    桑村 雅隆
    Single work, 裳華房, Nov. 2008, Japanese
    Textbook

■ Lectures, oral presentations, etc.
  • Conservation breaking dynamics in reaction-diffusion systems
    KUWAMURA MASATAKA
    ICIAM2015, Aug. 2015, English, Beijing, China, International conference
    [Invited]
    Oral presentation

  • 散逸系におけるパターン選択問題について
    KUWAMURA, Masataka
    日本数学会春期応用数学分科会特別講演, 2004, Japanese, 日本数学会, 筑波,, Domestic conference
    [Invited]
    Invited oral presentation

■ Affiliated Academic Society
  • 日本数学会

■ Research Themes
  • 特異摂動法の新しい理論と応用ー細胞極性に関する反応拡散方程式モデルの数理解析ー
    桑村 雅隆
    日本学術振興会, 科学研究費助成事業, 基盤研究(C), 神戸大学, 01 Apr. 2024 - 31 Mar. 2029

  • Mass-conserving reaction-diffusion systems and their perturbation
    Kuwamura Masataka
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Kobe University, Apr. 2016 - Mar. 2023
    In this research, I studied mass-conserving reaction-diffusion systems which are mathematical models for the polarity formation of cells. First, I investigated the dynamics of a localized unimodal pattern in mass-conserving reaction-diffusion systems, and provided mathematical characterizations of the motion of the localized unimodal pattern. Next, I investigated the oscillatory dynamics and bifurcation structure of a mass-conserving reaction-diffusion system with bistable nonlinearity, and showed that it exhibits four different spatiotemporal patterns including two types of oscillatory patterns, My research was based on a joint work with Professors Hirofumi Izuhara (Miyazaki),Sungrim Seirin-Lee (Kyoto) and Shin-Ichiro Ei (Hokkaido), and my results were published in Chaos, vol.27 (2017), SIAM Journal on Applied Mathematics, vol.78 (2018) and Journal of Mathematical Biology, vol.84 (2022).

  • Pattern dynamics in dissipative systems and their related topics
    KUWAMURA Masataka, OGAWA Toshiyuki
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Kobe University, Apr. 2010 - Mar. 2014
    We investigated properties of solutions of prey-predator system with dormant predators. Moreover, we proposed a mathematical model for the differentiation and proliferation of Drosophila intestinal stem cells.

  • 石井 克幸
    科学研究費補助金／基盤研究(C), 2010
    Competitive research funding

  • Hamiltonian structure in the pattern selection problems of dissipative systems
    KUWAMURA Masataka, EI Shin-ichiro, OGAWA Toshiyuki
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Kobe University, 2006 - 2009
    We studied the gradient/skew-gradient structure that enables us to apply the Hamiltonian formalism for studying the stability of stationary solutions in reaction-diffusion systems in various pattern formation problems. Moreover, we studied the stabilizing effect of dormancy of predators on the population dynamics of prey-predator systems.

  • 内藤 雄基
    科学研究費補助金／基盤研究(C), 2008
    Competitive research funding

  • 勾配・歪勾配構造をもつ散逸系における時空間周期パターンの解析
    桑村 雅隆, 小川 知之, 柳田 英二
    日本学術振興会, 科学研究費助成事業, 萌芽研究, 神戸大学, 2003 - 2005
    勾配・歪勾配構造は散逸系にハミルトン構造を自然に導くものである。この構造をもつ散逸系においては、時空間周期パターンの安定性は極めて単純で自然な公式によって決定される。この結果は、柳田教授との共著論文として、Physica D 175(2003)pp.185-195において発表した。また、多数の安定な空間周期パターンのうち、現実的にどの空間周期をもったパターンが最も高い確率で現れるのかというパターン選択問題を、勾配・歪勾配構造をもつ散逸系の場合に調べた。とくにパターン選択の基本原理ではないかと予想されている「臨界安定性仮説」を本研究の補助金によって購入したパソコンを利用した数値実験によって検証した。幸運にも、2004年度の春の日本数学会応用数学分科会(筑波大学)の特別講演者に推薦されたこともあり、この結果を学会の特別講演の形で発表することができた。この結果をまとめた論文は、SIAM J.Appl.Math.65(2005)pp.618-643において発表した。本年度は、これらの一連の研究に引き続いて、九州大学数理学研究院の栄伸一郎教授と龍谷大学理工学部の森田善久教授との共同研究を行い、反応拡散方程式に現れる特異摂動問題をハミルトン構造の視点から調べて、その成果をPhysica D 207(2005)pp.171-219で発表することができた。また、2005年度の秋の日本数学会応用数学分科会(岡山大学)でも研究発表することができた。一方、研究分担者の小川は、ミシャイコフ教授らのグループとの共同研究でSwift-Hohenberg方程式の分岐ダイアグラムを詳細に調べることに成功した。その結果は、SIAM J.Appl.Dyn.Sys.4(2005)pp.1-31において発表された。

  • 内藤 雄基
    科学研究費補助金／基盤研究(C), 2005
    Competitive research funding

  • 船越 俊介
    科学研究費補助金／基盤研究(B), 2005
    Competitive research funding

  • 石井 克幸
    科学研究費補助金／基盤研究(C), 2005
    Competitive research funding

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