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 本論文之主旨在嘗試了解Lotka-Volterra模型中,三個物種之間生態競爭的動態行為與過程.此模型之特性是在生態上相互剋制;即三個物種中若其中之一消失,則在兩兩競爭之下,第一個物種將淘汰第三個物種,第二個物種將淘汰第二個物種,第二個物種將淘汰第一個物種.利用Hopf分歧理論以及藉助數學軟體Matlab做數值分析,我們找出許多不同的周期解,其中包括擴散性對此系統周期解的影響.
 The aim of this thesis is to study the dynamics of Lotka-Volterra competition model with three species. This model cooresponds to the biological circumstance where in purely pirwise competition 1 beats 3, 3 beats 2 and 2 beats 1. With the aid of Hopf bifurcation, we found various periodic solutions numerically by making use of Matlab. Furthermore, diffusion on such systems has also been investigated.
 1. Introduction........................................1 2. A Hopf bifurcation result...........................9 3. Numerical study on periodic solutions..............23 4. Diffusion influence................................27 5. Reference..........................................34
 [B] P. N. Brown, Decay to uniform states in ecological interactions, SIAM J. Appl. Math. Vol. 38 (1980), No. 1, 22-37.[CHW] C. W. Chi, S. B. Hsu and L. I. Wu, On the unsymmetric May-Leonard model of three competing species, SIAM J. Appl. Math. 58 (1998), No. 1, 211-226 (Electronic).[EIM] S. I. Ei, R. Ikota and M. Mimura, Segregating partition problem in competition-diffusion systems, Interface and free boundaries, Vol. 1 (1999), 57-80.[H] M. W. Hirsch, System of differential equations which are competitive and cooperative .I: Limit set, SIAM J. Math. Anal. 13 (1982), 167-179.[M] J. D. Murray, Mathematical biology, Springer-Verlag, 1993.[ML] May R. M. and W. J. Leonard, Nonlinear aspects of competition between three species, SIAM J. Appl. Math. 29 (1975), 243-253.[MM] Marsden J. and M. McCraken, The Hopf bifurcation and its applications, Appl. Math. Sci., Vol. 19 (1996), Spring-Verlag, NewYork.[P] Paul Waltman, Competition models in population biology, SIAM, 1983.[S] H. Smith, Periodic orbits of competitive and cooperative systems, J. Diff. Eq. 65 (1986), 361-373.[W] P. Waltman, Competition models in population biology, SIAM, Philadelphia, 1983.[Z] Zeeman M. L., Hopf bifurcations in competitive three-dimensional Lotka-Volterra system, Dynamics and Stability of Systems, 8 (1993), 189-217.[ZP] L. Zhou and C. V. Pao, Asymptotic behavior of a competitive-diffusion system in population dynamics, Nonlinear Analysis, Theory, Methods and Applications, Vol. 38 (1980), No. 1, 22-37.
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