Research activity information

• Sep. 2009 日本応用数理学会, 日本応用数理学会論文賞, Japan Journal of Industrial and Applied Mathematics, vol 25, pp.281-303 (2008) に掲載された論文

  Masataka Kuwamura

• 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


• Oscillations and bifurcation structure of reaction–diffusion model for cell polarity formation

  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)


• Diffusion-driven destabilization of spatially homogeneous limit cycles in reaction-diffusion systems

  Masataka Kuwamura, Hirofumi Izuhara

  We study the diffusion-driven destabilization of a spatially homogeneous limit cycle with large amplitude in a reaction-diffusion system on an interval of finite size under the periodic boundary condition. Numerical bifurcation analysis and simulations show that the spatially homogeneous limit cycle becomes unstable and changes to a stable spatially nonhomogeneous limit cycle for appropriate diffusion coefficients. This is analogous to the diffusion-driven destabilization (Turing instability) of a spatially homogeneous equilibrium. Our approach is based on a reaction-diffusion system with mass conservation and its perturbed system considered as an infinite dimensional slow-fast system (relaxation oscillator). Published by AIP Publishing.

  AMER INST PHYSICS, 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

  In this paper, we study the stability of a coexistence equilibrium in a prey-predator system with dormancy of predators. The results suggest that dormancy of predators can stabilize the population dynamics of prey-predator systems if the switch to predators entering dormancy is very sharp or if both the hatching and mortality rates of dormant predators are sufficiently low.

  KOBE UNIV, DEPT MATHEMATICS, 2014, Funkcialaj ekvacioj. Serio internacia, 57(2) (2), 339 - 350, English

  [Refereed]

  Scientific journal


• Mathematical modelling and experiments for the proliferation and differentiation of Drosophila intestinal stem cells II

  Masataka Kuwamura, Kousuke Maeda, Takashi Adachi-Yamada

  The Drosophila posterior midgut epithelium mainly consists of intestinal stem cells (ISCs); semi-differentiated cells, i.e. enteroblasts (EBs); and two types of fully differentiated cells, i.e. enteroendocrine cells (EEs) and enterocytes (ECs), which are controlled by signalling pathways. In [M. Kuwamura, K. Maeda, and T. Adachi-Yamada, Mathematical modeling and experiments for the proliferation and differentiation of Drosophila intestinal stem cells I, J. Biol. Dyn. 4 (2009), pp. 248-257], on the basis of the functions of the Wnt and Notch signalling pathways, we studied the regulatory mechanism for the proliferation and differentiation of ISCs under the assumption that the Wnt proteins are supplied from outside the cellular system of ISCs. In this paper, we experimentally show that the Wnt proteins are specifically expressed in ISCs, EBs, and EEs, and theoretically show that the cellular system of ISCs can be self-maintained under the assumption that the Wnt proteins are produced in the cellular system of ISCs. These results provide a useful basis for determining whether an environmental niche is required for maintaining the cellular system of tissue stem cells.

  TAYLOR & FRANCIS LTD, 2012, Journal of Biological Dynamics, 6(2) (2), 267 - 276, English

  [Refereed]

  Scientific journal


• Implications of resting eggs of zooplankton for the paradox of enrichment

  Takefumi Nakazawa, Masataka Kuwamura, Norio Yamamura

  In this study, we numerically investigated to what extent introducing resting-egg dynamics would stabilize simple Daphnia-algae consumer-resource models. In the models, the density of viable resting eggs was explicitly expressed, and we assumed that zooplankton produced resting eggs seasonally or in response to food deficiency and that resting eggs hatched seasonally. The models predicted that, although the paradox of enrichment was not completely resolved (i.e., the system was destabilized by eutrophication), we found the following conditions under which the stabilizing effects of resting eggs would be significantly large: (1) resting eggs are produced seasonally (rather than in response to food deficiency), (2) the annual average allocation ratio to resting eggs is large, and (3) the annual average hatching rate of resting eggs is low. The results suggest that resting-egg dynamics can significantly reduce the paradox of enrichment within the biologically meaningful parameter space and contribute to the stability of plankton community dynamics.

  SPRINGER TOKYO, 2011, Population Ecology, 53(2) (2), 341 - 350, English

  [Refereed]

  Scientific journal


• Dormancy of predators dependent on the rate of variation in prey density

  Masataka Kuwamura, Takefumi Nakazawa

  In this paper, a simple model is used to demonstrate that the dormancy of predators dependent on the rate of decline in the prey density can strongly stabilize the population dynamics of prey-predator systems. This result may help explain why the population dynamics of phytoplankton-zooplankton (-resting eggs) is frequently observed to be strongly stable in nature. Moreover, it is numerically shown that the model can have two stable prey-predator cycles with different amplitudes and periods, which suggests that prey-predator (-dormant predator) systems have the potential to generate multiple stable cycles without any other mechanism.

  SIAM PUBLICATIONS, 2011, SIAM Journal on Applied Mathematics, 71(1) (1), 169 - 179, English

  [Refereed]

  Scientific journal


• Mathematical modelling and experiments for the proliferation and differentiation of Drosophila intestinal stem cells I

  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


• A minimum model of prey-predator system with dormancy of predators and the paradox of enrichment

  Masataka Kuwamura, Takefumi Nakazawa, Toshiyuki Ogawa

  In this paper, a mathematical model of a prey-predator system is proposed to resolve the paradox of enrichment in ecosystems. The model is based on the natural strategy that a predator takes, i.e, it produces resting eggs in harsh environment. Our result gives a criterion for a functional response, which ensures that entering dormancy stabilizes the population dynamics. It is also shown that the hatching of resting eggs can stabilize the population dynamics when the switching between non-resting and resting eggs is sharp. Furthermore, the bifurcation structure of our model suggests the simultaneous existence of a stable equilibrium and a large amplitude cycle in natural enriched environments. © 2008 Springer-Verlag.

  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


• Hamiltonian Formalism in Pattern Formation Problems in Dissipative Systems

  KUWAMURA, Masataka

  Mar. 2006, 応用数理, 16(1) (1), 17 - 26, Japanese

  [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


• On the turing patterns in one-dimensional gradient/skew-gradient dissipative systems

  M Kuwamura

  In this article, fundamental properties concerning the Turing patterns are considered in one-dimensional dissipative systems with gradient/skew-gradient structure introduced in [ M. Kuwamura and E. Yanagida, Phys. D, 175 ( 2003), pp. 185 - 195]. It is a natural extension of free energy, which covers reaction-diffusion systems of activator-inhibitor type. The theory based on this concept provides a new perspective on a fundamental problem of what unique Turing pattern is to be selected among many.

  SIAM PUBLICATIONS, 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

  The concept of gradient/skew-gradient structure-an extension of free energy-is introduced. In dissipative systems with this structure, the Eckhaus and zigzag instability criteria can be represented in terms of first integral and free energy per unit length for steady states. Moreover, an exact relation between these criteria is presented. These results are valid for steady states of arbitrary profile and amplitude, which implies that the instability criteria are valid for steady states far from threshold. Furthermore, our results support the marginal stability hypothesis for roll solutions in the wavenumber selection problem in gradient systems. The derivation for the results is simple and rigorous. (C) 2002 Elsevier Science B.V. All rights reserved.

  ELSEVIER SCIENCE BV, 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

  A stability criterion of roll solutions of the two-dimensional Swift-Hohenberg equation is presented. It clarifies the effect of the system size on the primary instabilty of rolls. An interpretation of the phase-diffusion equation is also given from the viewpoint of spectral analysis. The key to carrying out the spectral analysis is that the infinite-dimensional system of linear equations naturally induced by the Fourier decomposition for the linearized eigenvalue problem of the roll solution can be reduced to the three-dimensional system.

  SIAM PUBLICATIONS, 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

• ハミルトン構造とパターン形成

  KUWAMURA, Masataka

  Apr. 2005, 物性研究, vol.84 No.1, 2-21, Japanese

  Introduction scientific journal

• 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

• Single transition layer in mass-conserving reaction-diffusion systems with bistable nonlinearity

  桑村雅隆

  RIMS 共同研究（公開型） 常微分方程式の定性的理論の構築とその汎用性の探究, Oct. 2024, Japanese

  [Invited]

  Oral presentation


• Periodic solutions of mass-conserving reaction-diffusion systems and their perturbed systems

  Masataka Kuwamura

  Turing Symposium on Morphogenesis 2024, Feb. 2024, English

  [Invited]

  Invited oral presentation


• 保存量をもつ反応拡散方程式系における特異摂動問題について

  桑村雅隆

  反応拡散系パターンダイナミクスの新展開, Jun. 2023, Japanese

  [Invited]

  Invited oral presentation


• 保存量をもつ反応拡散方程式系における特異摂動問題について

  桑村雅隆

  OCAMI共同研究 「反応拡散方程式と非線形分散型方程式の解の挙動」, Feb. 2023

  [Invited]

  Invited oral presentation


• 保存量をもつ反応拡散方程式系における特異摂動問題について

  桑村雅隆

  Okayama Workshop on Partial Differential Equations, Oct. 2022

  [Invited]

  Invited oral presentation


• 細胞極性化に関連する微分方程式の解の性質について

  明治大学MIMS共同研究集会「幾何学・連続体力学・情報科学の交差領域の探索」, Dec. 2020

  [Invited]


• 保存量をもつ反応拡散系における特異摂動の例について

  桑村雅隆

  OCAMI共同研究「反応拡散方程式と非線形分散型方程式の解の挙動」, Feb. 2020, Japanese

  [Invited]

  Invited oral presentation


• Dynamics of localized patterns in reaction-diffusion systems for cell polarization by extracellular signaling

  KUWAMURA MASATAKA

  The 43rd Sapporo Symposium on Partial Differential Equations, Aug. 2018, English, International conference

  [Invited]

  Invited oral presentation


• 保存量をもつ反応拡散系におけるパルス状局在解の挙動について

  KUWAMURA MASATAKA, Lee Seirin, Ei Shin-ichiro

  2017年度応用数学合同研究集会, Dec. 2017, Japanese, Domestic conference

  Oral presentation


• Diffusion driven destabilization of a spatially homogeneous limit cycle in reaction-diffusion systems

  KUWAMURA MASATAKA

  JSMB2016, Sep. 2016, English, Fukuoka, Japan, International conference

  Oral presentation


• Conservation breaking dynamics in reaction-diffusion systems

  KUWAMURA MASATAKA

  ICIAM2015, Aug. 2015, English, Beijing, China, International conference

  [Invited]

  Oral presentation


• 捕食者の休眠を伴う prey-predator 系に現れるTuring 不安定性について

  KUWAMURA MASATAKA

  生物数学の理論とその応用, Sep. 2014, Japanese, 京都大学数理解析研究所, Domestic conference

  Oral presentation


• Turing patterns in prey-predator systems with dormancy of predators

  KUWAMURA MASATAKA

  3rd Italian-Japanese workshop on geometric properties for parabolic and elliptic PDE's, Sep. 2013, English, Tokyo, International conference

  [Invited]

  Oral presentation


• Dormancy of predators in prey-predator systems

  Masataka Kuwamura

  The 7th East Asia SIAM Conference, Jun. 2011, English, Waseda University, Kitakyushu Campus, International conference

  Oral presentation


• Mathematical modeling and experiments for the proliferation and differentiation of Drosophila intestinal stem cells

  Masataka Kuwamura, Kousuke Maeda, Takashi Adachi-Yamada

  The second China-Japan Colloquim of Mathematical Biology, Aug. 2008, English, Okayama University, International conference

  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

• 日本数学会

• 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.


• 平均曲率流の近似問題と正則性・特異性に関する研究

  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.


• 非線形放物型方程式の自己相似性と解の特異性

  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。


• 非線形放物型偏微分方程式の自己相似構造と解の特異性

  内藤 雄基

  科学研究費補助金／基盤研究(C), 2005

  Competitive research funding


• 大学における数理情報教育に求められている課題の分析とその改善に関する研究

  船越 俊介

  科学研究費補助金／基盤研究(B), 2005

  Competitive research funding


• 数値計算アルゴリズムを用いた平均曲率流の解析的研究

  石井 克幸

  科学研究費補助金／基盤研究(C), 2005

  Competitive research funding