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Bacteriophageresistant and bacteriophagesensitive bacteria in a chemostat
Global analysis of a simple parasitehost model with homoclinic orbits
1.  Faculty of Science, Air Force Engineering University, Xi'an 710051, China, China 
2.  Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, China 
References:
[1] 
D. Ebert, M. Lipsitch and K. L. Mangin, The effect of parasites on host population density and extinction: Experimental epidemiology with Daphnia and six microparasites, American Naturalist, 156 (2000), 459477. doi: 10.1086/303404. 
[2] 
T.W. Hwang and Y. Kuang, Deterministic extinction effect of parasites on host populations, J. Math. Biol., 46 (2003), 1730. doi: 10.1007/s0028500201657. 
[3] 
Kaifa Wang and Y. Kuang, Fluctuation and extinction dynamics in hostmicroparasite systems, Comm. Pure Appl. Anal., 10 (2011), 15371548. doi: 10.3934/cpaa.2011.10.1537. 
[4] 
S. Hews, S. Eikenberry, J. D. Nagy and Y. Kuang, Rich dynamics of a hepatitis B viral infection model with logistic hepatocyte growth, J. Math. Biol., 60 (2010), 573590. doi: 10.1007/s0028500902783. 
[5] 
S. Eikenberry, S. Hews, J. D. Nagy and Y. Kuang, The dynamics of a delay model of HBV infection with logistic hepatocyte growth, Math. Biosc. Eng., 6 (2009), 283299. 
[6] 
F. Berezovsky, G. Karev, B. Song and C. CastilloChavez, A simple epidemic model with surprising dynamics, Math. Biosci. Eng., 2 (2005), 133152. 
[7] 
Z. Zhang, T. Ding, et al., "Qualitative Theory of Differential Equations," Translations of Mathematical Monographs, Vol. 101, Amer. Math. Soc., Providence, Rhode Island, 1992. 
[8] 
Zhien Ma and Jia Li, "Dynamical Modeling and Analysis of Epidemics," Singapore, 2009. 
show all references
References:
[1] 
D. Ebert, M. Lipsitch and K. L. Mangin, The effect of parasites on host population density and extinction: Experimental epidemiology with Daphnia and six microparasites, American Naturalist, 156 (2000), 459477. doi: 10.1086/303404. 
[2] 
T.W. Hwang and Y. Kuang, Deterministic extinction effect of parasites on host populations, J. Math. Biol., 46 (2003), 1730. doi: 10.1007/s0028500201657. 
[3] 
Kaifa Wang and Y. Kuang, Fluctuation and extinction dynamics in hostmicroparasite systems, Comm. Pure Appl. Anal., 10 (2011), 15371548. doi: 10.3934/cpaa.2011.10.1537. 
[4] 
S. Hews, S. Eikenberry, J. D. Nagy and Y. Kuang, Rich dynamics of a hepatitis B viral infection model with logistic hepatocyte growth, J. Math. Biol., 60 (2010), 573590. doi: 10.1007/s0028500902783. 
[5] 
S. Eikenberry, S. Hews, J. D. Nagy and Y. Kuang, The dynamics of a delay model of HBV infection with logistic hepatocyte growth, Math. Biosc. Eng., 6 (2009), 283299. 
[6] 
F. Berezovsky, G. Karev, B. Song and C. CastilloChavez, A simple epidemic model with surprising dynamics, Math. Biosci. Eng., 2 (2005), 133152. 
[7] 
Z. Zhang, T. Ding, et al., "Qualitative Theory of Differential Equations," Translations of Mathematical Monographs, Vol. 101, Amer. Math. Soc., Providence, Rhode Island, 1992. 
[8] 
Zhien Ma and Jia Li, "Dynamical Modeling and Analysis of Epidemics," Singapore, 2009. 
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