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桑村 雅隆大学院人間発達環境学研究科 人間環境学専攻教授
研究活動情報
■ 受賞- 2009年09月 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
- 2024年, Nonlinearity, 37, 115013, 英語Single Transition Layer in Mass-Conserving Reaction-Diffusion Systems with Bistable Nonlinearity[査読有り]研究論文（学術雑誌）
- Springer Science and Business Media LLC, 2022年, Journal of Mathematical Biology, 84(4) (4), 22, 英語[査読有り]研究論文（学術雑誌）
- 2018年, SIAM Journal on Applied Mathematics, 78(6) (6), 3238 - 3257, 英語Dynamics of localized unimodal patterns in reaction-diffusion systems for cell polarization by extracellular signaling[査読有り]研究論文（学術雑誌）
- 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年03月, CHAOS, 27(3) (3), 012908, 英語[査読有り]研究論文（学術雑誌）
- 2015年, Journal of Mathematical Biology, 71, 125 - 149, 英語Turing instabilities in prey-predator systems with dormancy of predators[査読有り]研究論文（学術雑誌）
- 2015年, Physical Review E, 92, 012908, 英語Perturbations and dynamics of reaction-diffusion systems with mass conservation[査読有り]研究論文（学術雑誌）
- Stability of Coexisting Equilibrium of Prey-Predator Systems with Dormancy of PredatorsIn 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年08月, FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 57(2) (2), 339 - 350, 英語[査読有り]研究論文（学術雑誌）
- 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年, JOURNAL OF BIOLOGICAL DYNAMICS, 6(2) (2), 267 - 276, 英語[査読有り]研究論文（学術雑誌）
- 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年, JOURNAL OF BIOLOGICAL DYNAMICS, 6(2) (2), 267 - 276, 英語[査読有り]研究論文（学術雑誌）
- 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年04月, POPULATION ECOLOGY, 53(2) (2), 341 - 350, 英語[査読有り]研究論文（学術雑誌）
- 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年, SIAM JOURNAL ON APPLIED MATHEMATICS, 71(1) (1), 169 - 179, 英語[査読有り]研究論文（学術雑誌）
- 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年03月, Journal of Mathematical Biology, 58(3) (3), 459 - 479, 英語[査読有り]研究論文（学術雑誌）
- 2009年, Chaos, , vol. 19, 043121, 英語Mixed-mode oscillations and chaos in a prey-predator system with dormancy of predators[査読有り]研究論文（学術雑誌）
- 2008年, Japan Journal of Industrial and Applied Mathematics, , vol. 25, pp.281-303, 英語Deviation from the predicted wavenumber in a mode selection problem for the Turing patterns[査読有り]研究論文（学術雑誌）
- 2007年, Advanced Studies in Pure Mathematics, , vol. 47, pp.635-646, 英語The Hamiltonian formalism in reaction-diffusion systems[査読有り]研究論文（学術雑誌）
- 2006年03月, 応用数理, vol.16 No.1, 17-26, 日本語散逸系のパターン形成問題に現れるハミルトン形式[査読有り]研究論文（学術雑誌）
- 2006年, Journal of Differential Equations, , vol. 230, pp.446-464, 英語Krein's formula for indefinite multipliers in linear periodic Hamiltonian systems[査読有り]研究論文（学術雑誌）
- 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年, SIAM JOURNAL ON APPLIED MATHEMATICS, 65(2) (2), 618 - 643, 英語[査読有り]研究論文（学術雑誌）
- 2005年, Physica D, , vol.207, pp.171-219, 英語A variational approach to singular perturbation problems in reaction-diffusion systems[査読有り]研究論文（学術雑誌）
- The Eckhaus and zigzag instability criteria in gradient/skew-gradient dissipative systemsThe 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年02月, PHYSICA D-NONLINEAR PHENOMENA, 175(3-4) (3-4), 185 - 195, 英語[査読有り]研究論文（学術雑誌）
- 2001年, Japan Journal of Industrial and Applied Mathematics, , vol.18, pp.739-768, 英語A perspective of renormalization group approaches[査読有り]研究論文（学術雑誌）
- The stability of roll solutions of the two-dimensional Swift-Hohenberg equation and the phase-diffusion equationA 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年09月, SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 27(5) (5), 1311 - 1335, 英語[査読有り]研究論文（学術雑誌）
- 1994年, Journal of Dynamics and Differential Equations, , vol.6, pp.185-225, 英語Phase dynamics method with applications to the Swift-Hohenberg equation[査読有り]研究論文（学術雑誌）
- 1992年, Japan Journal of Industrial and Applied Mathematics, , vol.9, pp.35-77, 英語Very slow dynamics for some reaction-diffusion system with activator-inhibitor type[査読有り]研究論文（学術雑誌）
■ 書籍等出版物
- 単著, 裳華房, 2018年11月, 日本語応用解析概論教科書・概説・概論
- 単著, 裳華房, 2016年02月, 日本語線形代数学入門教科書・概説・概論
- 単著, 共立出版, 2015年01月, 日本語パターン形成と分岐理論学術書
- 単著, 裳華房, 2008年11月, 日本語微分積分入門教科書・概説・概論
- Turing Symposium on Morphogenesis 2024, 2024年02月, 英語Periodic solutions of mass-conserving reaction-diffusion systems and their perturbed systems[招待有り]口頭発表（招待・特別）
- 反応拡散系パターンダイナミクスの新展開, 2023年06月, 日本語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[招待有り]口頭発表（招待・特別）
- 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」, 2023年02月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[招待有り]口頭発表（招待・特別）
- Okayama Workshop on Partial Differential Equations, 2022年10月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[招待有り]口頭発表（招待・特別）
- 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」, 2020年12月細胞極性化に関連する微分方程式の解の性質について[招待有り]
- 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」, 2020年02月, 日本語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[招待有り]口頭発表（招待・特別）
- The 43rd Sapporo Symposium on Partial Differential Equations, 2018年08月, 英語, 国際会議Dynamics of localized patterns in reaction-diffusion systems for cell polarization by extracellular signaling[招待有り]口頭発表（招待・特別）
- 2017年度応用数学合同研究集会, 2017年12月, 日本語, 国内会議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口頭発表（一般）
- JSMB2016, 2016年09月, 英語, Fukuoka, Japan, 国際会議Diffusion driven destabilization of a spatially homogeneous limit cycle in reaction-diffusion systems口頭発表（一般）
- ICIAM2015, 2015年08月, 英語, Beijing, China, 国際会議Conservation breaking dynamics in reaction-diffusion systems[招待有り]口頭発表（一般）
- 生物数学の理論とその応用, 2014年09月, 日本語, 京都大学数理解析研究所, 国内会議捕食者の休眠を伴う prey-predator 系に現れるTuring 不安定性について口頭発表（一般）
- 3rd Italian-Japanese workshop on geometric properties for parabolic and elliptic PDE's, 2013年09月, 英語, Tokyo, 国際会議Turing patterns in prey-predator systems with dormancy of predators[招待有り]口頭発表（一般）
- The 7th East Asia SIAM Conference, 2011年06月, 英語, Waseda University, Kitakyushu Campus, 国際会議Dormancy of predators in prey-predator systems口頭発表（一般）
- The second China-Japan Colloquim of Mathematical Biology, 2008年08月, 英語, Okayama University, 国際会議Mathematical modeling and experiments for the proliferation and differentiation of Drosophila intestinal stem cells口頭発表（一般）
- 日本数学会春期応用数学分科会特別講演, 2004年, 日本語, 日本数学会, 筑波,, 国内会議散逸系におけるパターン選択問題について[招待有り]口頭発表（招待・特別）
■ 共同研究・競争的資金等の研究課題