## SEARCH

Search Details### KUWAMURA MasatakaGraduate School of Human Development and Environment / Department of Human Environmental ScienceProfessor

#### Research activity information

■ Award- 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

- Springer Science and Business Media LLC, 2022, Journal of Mathematical Biology, 84(4) (4), 22, English[Refereed]Scientific journal
- 2018, SIAM Journal on Applied Mathematics, 78(6) (6), 3238 - 3257, English
**Dynamics of localized unimodal patterns in reaction-diffusion systems for cell polarization by extracellular signaling**[Refereed]Scientific journal - 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, Mar. 2017, CHAOS, 27(3) (3), 012908, English[Refereed]Scientific journal
- 2015, Journal of Mathematical Biology, 71, 125 - 149, English
**Turing instabilities in prey-predator systems with dormancy of predators**[Refereed]Scientific journal - 2015, Physical Review E, 92, 012908, English
**Perturbations and dynamics of reaction-diffusion systems with mass conservation**[Refereed]Scientific journal **Stability of Coexisting Equilibrium of Prey-Predator Systems with Dormancy of Predators**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, Aug. 2014, FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 57(2) (2), 339 - 350, English[Refereed]Scientific journal- 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
- 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
- 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, Apr. 2011, POPULATION ECOLOGY, 53(2) (2), 341 - 350, English[Refereed]Scientific journal
- 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
- 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.Mar. 2009, Journal of Mathematical Biology, 58(3) (3), 459 - 479, English[Refereed]Scientific journal
- 2009, Chaos, , vol. 19, 043121, English
**Mixed-mode oscillations and chaos in a prey-predator system with dormancy of predators**[Refereed]Scientific journal - 2008, Japan Journal of Industrial and Applied Mathematics, , vol. 25, pp.281-303, English
**Deviation from the predicted wavenumber in a mode selection problem for the Turing patterns**[Refereed]Scientific journal - 2007, Advanced Studies in Pure Mathematics, , vol. 47, pp.635-646, English
**The Hamiltonian formalism in reaction-diffusion systems**[Refereed]Scientific journal - Mar. 2006, 応用数理, vol.16 No.1, 17-26, Japanese
**Hamiltonian Formalism in Pattern Formation Problems in Dissipative Systems**[Refereed]Scientific journal - 2006, Journal of Differential Equations, , vol. 230, pp.446-464, English
**Krein's formula for indefinite multipliers in linear periodic Hamiltonian systems**[Refereed]Scientific journal - 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
- 2005, Physica D, , vol.207, pp.171-219, English
**A variational approach to singular perturbation problems in reaction-diffusion systems**[Refereed]Scientific journal **The Eckhaus and zigzag instability criteria in gradient/skew-gradient dissipative systems**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, Feb. 2003, PHYSICA D-NONLINEAR PHENOMENA, 175(3-4) (3-4), 185 - 195, English[Refereed]Scientific journal- 2001, Japan Journal of Industrial and Applied Mathematics, , vol.18, pp.739-768, English
**A perspective of renormalization group approaches**[Refereed]Scientific journal **The stability of roll solutions of the two-dimensional Swift-Hohenberg equation and the phase-diffusion equation**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, Sep. 1996, SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 27(5) (5), 1311 - 1335, English[Refereed]Scientific journal- 1994, Journal of Dynamics and Differential Equations, , vol.6, pp.185-225, English
**Phase dynamics method with applications to the Swift-Hohenberg equation**[Refereed]Scientific journal - 1992, Japan Journal of Industrial and Applied Mathematics, , vol.9, pp.35-77, English
**Very slow dynamics for some reaction-diffusion system with activator-inhibitor type**[Refereed]Scientific journal

■ Books And Other Publications

- Single work, 裳華房, Nov. 2018, Japanese
**応用解析概論**Textbook - Single work, 裳華房, Feb. 2016, Japanese
**線形代数学入門**Textbook - Single work, 共立出版, Jan. 2015, Japanese
**パターン形成と分岐理論**Scholarly book - Single work, 裳華房, Nov. 2008, Japanese
**微分積分入門**Textbook

- Turing Symposium on Morphogenesis 2024, Feb. 2024, English
**Periodic solutions of mass-conserving reaction-diffusion systems and their perturbed systems**[Invited]Invited oral presentation - 反応拡散系パターンダイナミクスの新展開, Jun. 2023, Japanese
**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**[Invited]Invited oral presentation - 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
**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**[Invited]Invited oral presentation - Okayama Workshop on Partial Differential Equations, Oct. 2022
**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**[Invited]Invited oral presentation - 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
**細胞極性化に関連する微分方程式の解の性質について**[Invited] - 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
**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**[Invited]Invited oral presentation - The 43rd Sapporo Symposium on Partial Differential Equations, Aug. 2018, English, International conference
**Dynamics of localized patterns in reaction-diffusion systems for cell polarization by extracellular signaling**[Invited]Invited oral presentation - 2017年度応用数学合同研究集会, Dec. 2017, Japanese, Domestic conference
**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**Oral presentation - JSMB2016, Sep. 2016, English, Fukuoka, Japan, International conference
**Diffusion driven destabilization of a spatially homogeneous limit cycle in reaction-diffusion systems**Oral presentation - ICIAM2015, Aug. 2015, English, Beijing, China, International conference
**Conservation breaking dynamics in reaction-diffusion systems**[Invited]Oral presentation - 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
**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**Oral presentation - 3rd Italian-Japanese workshop on geometric properties for parabolic and elliptic PDE's, Sep. 2013, English, Tokyo, International conference
**Turing patterns in prey-predator systems with dormancy of predators**[Invited]Oral presentation - The 7th East Asia SIAM Conference, Jun. 2011, English, Waseda University, Kitakyushu Campus, International conference
**Dormancy of predators in prey-predator systems**Oral presentation - The second China-Japan Colloquim of Mathematical Biology, Aug. 2008, English, Okayama University, International conference
**Mathematical modeling and experiments for the proliferation and differentiation of Drosophila intestinal stem cells**Oral presentation - 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
**散逸系におけるパターン選択問題について**[Invited]Invited oral presentation

■ Research Themes

- 学術研究助成基金助成金／基盤研究(C), Apr. 2016 - Mar. 2021, Principal investigatorCompetitive research funding
- 科学研究費補助金／基盤研究(C), 2010Competitive research funding
- 科学研究費補助金／基盤研究(C), 2010, Principal investigatorCompetitive research funding
- 科学研究費補助金／基盤研究(C), 2008Competitive research funding
- 科学研究費補助金／基盤研究(C), 2006, Principal investigatorCompetitive research funding
- 科学研究費補助金／基盤研究(C), 2005Competitive research funding
- 科学研究費補助金／基盤研究(B), 2005Competitive research funding
- 科学研究費補助金／基盤研究(C), 2005Competitive research funding
- 科学研究費補助金／萌芽研究, 2005, Principal investigatorCompetitive research funding