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$R_0$ and the global behavior of an agestructured SIS epidemic model with periodicity and vertical transmission
Global dynamics for twospecies competition in patchy environment
1.  Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan, Taiwan 
2.  Department of Mathematics, Mathematical Bioscience Institute, Ohio State University, Columbus, Ohio 43210 
References:
[1] 
R. S. Cantrell, C. Cosner and Y. Lou, Evolutionary stability of ideal free dispersal strategies in patchy environments,, J. Math. Biol., 65 (2012), 943. doi: 10.1007/s0028501104865. Google Scholar 
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S. A. Gourley and Y. Kuang, Twospecies competition with high dispersal: The winning strategy,, Math. Biosci. Eng., 2 (2005), 345. doi: 10.3934/mbe.2005.2.345. Google Scholar 
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S. B. Hsu, H. Smith and P. Waltman, Competitive exclusion and coexistence for competitive systems on ordered Banach spaces,, Trans. Amer. Math. Soc., 348 (1996), 4083. doi: 10.1090/S0002994796017242. Google Scholar 
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M. Y. Li and Z. Shuai, Globalstability problem for coupled system of differential equations on networks,, J. Differential Eqations., 248 (2010), 1. doi: 10.1016/j.jde.2009.09.003. Google Scholar 
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H. L. Smith, Competing subcommunities of mutualists and a generalized Kamke theorem,, SIAM J. Appl. Math., 46 (1986), 856. doi: 10.1137/0146052. Google Scholar 
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H. L. Smith, Monotone Dynamical Systems: An Introduction To The Theory of Competitive and Cooperative Systems,, Math. Surveys and Monographs, (1995). Google Scholar 
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Y. Takeuchi and Z. Lu, Permanence and global stability for competitive LotkaVolterra diffusion systems,, Nonlinear Anal., 24 (1995), 91. doi: 10.1016/0362546X(94)E0024B. Google Scholar 
show all references
References:
[1] 
R. S. Cantrell, C. Cosner and Y. Lou, Evolutionary stability of ideal free dispersal strategies in patchy environments,, J. Math. Biol., 65 (2012), 943. doi: 10.1007/s0028501104865. Google Scholar 
[2] 
B. S. Goh, Global stability in manyspecies systems,, American Naturalist, 111 (1977), 135. doi: 10.1086/283144. Google Scholar 
[3] 
S. A. Gourley and Y. Kuang, Twospecies competition with high dispersal: The winning strategy,, Math. Biosci. Eng., 2 (2005), 345. doi: 10.3934/mbe.2005.2.345. Google Scholar 
[4] 
S. B. Hsu, H. Smith and P. Waltman, Competitive exclusion and coexistence for competitive systems on ordered Banach spaces,, Trans. Amer. Math. Soc., 348 (1996), 4083. doi: 10.1090/S0002994796017242. Google Scholar 
[5] 
M. Y. Li and Z. Shuai, Globalstability problem for coupled system of differential equations on networks,, J. Differential Eqations., 248 (2010), 1. doi: 10.1016/j.jde.2009.09.003. Google Scholar 
[6] 
H. L. Smith, Competing subcommunities of mutualists and a generalized Kamke theorem,, SIAM J. Appl. Math., 46 (1986), 856. doi: 10.1137/0146052. Google Scholar 
[7] 
H. L. Smith, Monotone Dynamical Systems: An Introduction To The Theory of Competitive and Cooperative Systems,, Math. Surveys and Monographs, (1995). Google Scholar 
[8] 
Y. Takeuchi and Z. Lu, Permanence and global stability for competitive LotkaVolterra diffusion systems,, Nonlinear Anal., 24 (1995), 91. doi: 10.1016/0362546X(94)E0024B. Google Scholar 
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