簡易檢索 / 詳目顯示

研究生: 宋宥松
Sung,You-Song
論文名稱: 環境對物種遷移的影響
The migration of single species in a logistic model
指導教授: 陳兆年
Chen, Chao Nien
口試委員: 曾旭堯
Tzeng, Shyuh Yaur
蔡英士
Choi,Yung-Sze
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系
Department of Mathematics
論文出版年: 2017
畢業學年度: 105
論文頁數: 28
中文關鍵詞: 空間生態學反應擴散方程變分法
外文關鍵詞: spatial ecology, reaction-diffusion systems, variational method
相關次數: 點閱:2下載:0
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • 本篇論文主要探討當物種在不同環境對其生物總量所造成的影響。當一個環境中資源分布差異懸殊時,相對於資源均勻分佈的環境下所能維持的生物總量將會比較大。我們考慮不同種類的異質性環境,估計在何種情況下其生物總量所能達到的最大效益。


    In this thesis, a single species logistic model is used to study the heterogeneity e ects
    to migration. If dispersal is allowed, the population in an environment in which resources
    vary spatially will reach a higher total equilibrium biomass than that in an environment in
    which the same total resources are distributed homogeneously. We consider several examples
    for heterogeneous distribution of resources and give some estimates for the total equilibrium
    biomass.

    1 Introduction 2 2 Existence and uniqueness results 3 3 Basic properties for the positive solution 6 4 A lower bound of total equilibrium biomass 8 5 Some properties for the pro le of ud 9 6 An upper bound of total equilibrium biomass 11 7 Jump type heterogeneity 12 8 A piecewise linear approximation 17 9 Final remarks 23 References 26

    [1] X. Bai, X. He and F. Li, An optimization problem and its application in population
    dynamics. Proceeding of the American Mathematical Society (2016), 2161-2170.
    [2] R.S. Cantrell and C. Cosner, Spatial ecology via reaction-di
    usion equations, Series
    in Mathematical and Computational Biology, Wiley, Chichester, UK (2003).
    [3] T. K. Callahan and E. Knobloch, Pattern formation in three-dimensional reaction-
    di
    usion system, Phys. D 132 (1999), 339-362.
    [4] C.-N. Chen, Multiple solutions for a class of nonlinear Sturm-Liouville problems on
    the half line, J. Di
    erential Equations 85 (1990), 236-275.
    [5] C.-N. Chen, Uniqueness and bifurcation for solutions of nonlinear Sturm-Liouville
    eigenvalue problems, Arch. Rational. Mech. Anal. 111 (1990), 51-85.
    [6] C.-N. Chen, Multiple solutions for a class of nonlinear Sturm-Liouville problems
    when nonlinearities are not odd, J. Di
    erential Equations 89 (1991), 138-153.
    [7] C.-N. Chen, Some existence and bifurcation results for solutions of nonlinear Sturm-
    Liouville eigenvalue problems, Math. Zeitschrift 208 (1991), 177-192.
    [8] C.-N. Chen, Uniquencess of solutions of some second order di
    erential equations,
    Di
    erential & Integral Equations 6 (1993), 825-834.
    [9] C.-N. Chen and S.-Y. Tzeng, Some properties of Palais-Smale sequences with applica-
    tions to elliptic boundary-value problems, Electronic Journal of Di
    erential Equations
    17 (1999), 1-29.
    [10] C.-N. Chen and Y. S. Choi., Standing pulse solutions to FitzHugh-Nagumo equations,
    Arch. Rational. Mech. Anal. 206 (2012), 741-777.
    [11] C.-N. Chen. and Y. S. Choi, Traveling pulse solutions to FitzHugh-Nagumo equations,
    Calculus of Variations and Partial Di
    erential Equations 54 (2015), 1-45.
    [12] C.-N. Chen, S.-I. Ei, Y.-P. Lin, and S.-Y. Kung, Standing waves joining with Turing
    patterns in FitzHugh-Nagumo type systems, Communications in Partial Di
    erential
    Equations 36 (2011), 998-1015.
    [13] C.-N. Chen and X. Hu, Maslov index for homoclinic orbits of Hamiltonian systems,
    Ann. Inst. H. Poincare Anal. Non Linearie 24 (2007), 589{603.
    The migration of single species in a logistic model 27
    [14] C.-N. Chen and X. Hu, Stability analysis for standing pulse solutions to FitzHugh{
    Nagumo equations, Calculus of Variations and Partial Di
    erential Equations 49
    (2014), 827{845.
    [15] C.-N. Chen. and X. Hu, Stability criteria for reaction-di
    usion systems with skew-
    gradient structure, Communications in Partial Di
    erential Equations 33 (2008), no.
    2, 189-208.
    [16] C.-N. Chen, S.-I. Ei and Y.-P. Lin, Turing patterns and wavefronts for reaction-
    di
    usion systems in an in
    nite channel, SIAM J. Appl. Math. 70 (2010), 2822-2843.
    [17] C.-N. Chen, Y. Morita, and S.-Y. Kung, Planar standing wavefronts in the FitzHugh-
    Nagumo equations, SIAM J. Math. Anal. 46 (2014), 657-690.
    [18] C.-N. Chen and K. Tanaka, A variational approach for standing waves of FitzHugh-
    Nagumo type systems, J. Di
    erential Equations 257 (2014), 109-144.
    [19] C.-N. Chen, S. Jimbo and Y. Morita, Spectral comparison and gradient-like property
    in the FitzHugh-Nagumo type equations, Nonlinearity 28 (2015), 1003-1016.
    [20] C.-N. Chen, C.-C. Chen and C.-C. Huang, Traveling waves for the FitzHugh-Nagumo
    system on an in
    nite channel, J. Di
    erential Equations 261 (2016), 3010-3041.
    [21] C.-N. Chen, P. van Heijster, Y. Nishiura and T. Teramoto Localized patterns in a
    three-component FitzHugh-Nagumo model revisited via an action functional, J. Dyn.
    Di
    er. Equ., (2016) DOI 10.1007/s10884-016-9557-z.
    [22] D. L. DeAngelis,W.-M. Ni and B. Zhang, Dispersal and spatial heterogeneity : single
    species, J. Math. Biol.(2016)72:239-254.
    [23] L. C. Evans, Partial di
    erential equations, Graduate Studies in Mathematics, volume
    19 (1991).
    [24] P. C. Fife, Mathematical Aspects of Reacting and Di
    using Systems. Springer, Berlin,
    1979.
    [25] I. M. Gelfand and S. V. Fomin, Calculus of variation, Moscow State University
    (1963).
    [26] A. Gierer and H. Meinhardt, A theory of biological pattern formation, Kybernetik 12
    (1972), 30-39.
    [27] P. Gray and S. K. Scott, Autocatalytic reaction in the isothermal, contonuous stirred
    tank reactor: Oscillations and instabilities in the system A + 2B ! 3B, B ! C,
    Chem. Engrg. Sci. 39 (1984), 1087-1097.
    [28] D. Horstmann, From 1970 until present: The Keller-Segel model in chemotaxis and
    its consequences, Jahresber. Deutsch. Math.-Verein. 105 (2003), 103-165.
    [29] E. F. Keller and L. A. Segel, lnitiation of slime mold aggregation viewed as an insta-
    bility, J. Theoret. Biol. 26 (1970), 399-415.
    [30] Y. Lou, On the e
    ects of migration and spatial heterogeneity on single and multiple
    species, J. Di
    erential Equation 223 (2006), 400-426.
    [31] K. J. Lee, W. D. McCormick, J. E. Pearson, and H. L. Swinney, Experimental
    observation of self-replicating spots in a reaction-di
    usion system, Nature 369 (1994),
    215-218.
    [32] I. Lengyel and I. R. Epstein, Modeling of Turing structures in the chlorite-iodide-
    malonic-acid-starch reaction system, Science 251 (1991), 650-652.
    [33] I. Lengyel and I. R. Epstein, A chemical approach to designing Turing patterns in
    reaction-di
    usion systems, Proc. Nat. Acad. Sci. U.S.A. 89 (1992), 3977-3979.
    [34] W.-M. Ni, The mathematics of di
    usion, CBMS-NSF Reginal Conf. Ser. in Appl.
    Math.82, SIAM, Philadelphia (2011), 66-70.
    [35] M.-H. Protter, H.-F. Weinberger, Maximum principles in di
    erential equations
    Springer-Verlag, New York, Berlin(1984), 1-7.
    [36] P. H. Rabinowitz, Minimax methods in critical point theory with applications to
    di
    erential equations, CBMS Regional Conference Series in Mathematics, 65 (1986).
    [37] J. Smoller, Shock waves and reaction-di
    usion equations, Second edition.
    Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical
    Sciences], 258. Springer-Verlag, New York (1994).
    [38] A. M. Turing, The chemical basis of morphogenesis, Phil. Trans. R. Soc. Lond. B
    237 (1952), 37-72.

    無法下載圖示 全文公開日期 本全文未授權公開 (校內網路)
    全文公開日期 本全文未授權公開 (校外網路)

    QR CODE