臺灣博碩士論文加值系統

摘 要
在探討生態物種競爭的行為與過程，Latka-Volterra所提出的模型已被廣泛的研究。在本篇論文中，我們研究的是3種物種競爭的情形，我們探討在何種情況下有非一致分佈共存解的穩定狀態。

Abstract
The Latka-Volterra system is the first model of interacting populations to be considerd. In this thesis,we study the co- existence of the Latka-Volterra system when there are three competing species. We are interesting in the coexistence of non-uniformly distributed steady states.

Contents
1.Introduction...............................1
2.Preliminary................................5
3.Simple Eigenvalue Bifurcatioon.............8
4.Global Bifurcatioon Result................ 14
5.References................................ 18

[1]L. Zhou and C. V. Pao, Asymptotic behavior of a competition-diffusion system in population
dynamics, Nonlinear Analysis, Theory, Methods \& Applications, Vol. 6, No. 11, pp. 1163-1184, 1982.
[2]Peter N. Brow, Decay to uniform states in ecological interactions, SIAM J. Appl. Math. Vol. 38, No, 1, pp. 22-37, 1980.
[3]Paul Waltman, Competition models in population biology, SIAM, 1983.
[4]J. D. Murray, Mathematical biology, springer, 1993.
[5]Crandall, M. G., and Rabinowitz, P. H., Bifurcation from simple eigenvalues,J. Funct. Anal. 8, 1971, pp. 321-340.
[6]Changfeng Gui and Yuan Lou, Uniqueness and Nonuniqueness of Coexistence States in theLotka-Volterra Competition Model, Communications on Pure and Applied Mathematics, Vol. XLVII, 1571-1594 (1994).
[7]Chi, Chia-Wei; Hsu, Sze-Bi; Wu, Lih-Ing On the asymmetric May-Leonard of threecompeting species, SIAM J. Appl. Math. 58 (1998), no. 1, 211-226 (electronic).
[8]M. L. Zeeman, Hopf bifurcations in competitive three-dimensional Lotka-Volterra systems,Dynamics and Stability of systems Vol. 8, No. 3, pp. 189-217, 1993.
[9]Masayasu Mimura and Paul C. Fife, A 3-component system of competition and diffusion, Hiroshima. Math. J. 16 (1986), 189-207.
[10]Gilbarg,D.,and Trudinger,n.s.,Elliptic Partial Differential Equation of Second Order,2nded.,Springer-Verlag,Berlin,New York,1983.
[11]Murray H.Protter.,and Hans F.Weinberger.,Maximum Principles in Differential Equations,Springer-Verlag.Berlin,New York.