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 |
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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 eects
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] 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.