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Asymptotic behavior of a ratiodependent predatorprey system with disease in the prey
1.  Department of Information and Mathematics, Korea University, Jochiwon 339700, South Korea, South Korea 
2.  Department of Mathematics Education, Cheongju University, Cheongju, Chungbuk 360764, South Korea 
References:
[1] 
R. Arditi and L. R. Ginzburg, Coupling in predatorprey dynamics: ratio dependence,, J. Theor. Biol. 139 (1989), (1989), 311. Google Scholar 
[2] 
R. Arditi, L. R. Ginzburg and H. R. Akcakaya, Variation in plankton densities among lakes: a case for ratiodependent models,, American Naturalist 138 (1991), (1991), 1287. Google Scholar 
[3] 
R. Arditi and H. Saiah, Empirical evidence of the role of heterogeneity in ratiodependent consumption,, Ecology 73 (1992), (1992), 1544. Google Scholar 
[4] 
R. S. Cantrell and C. Cosner, On the dynamics of predatorprey models with the BeddingtonDeAngelis functional response,, J. Math. Anal. Appl. 257 (2001), (2001), 206. Google Scholar 
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C. Cosner, D. L. DeAngelis, J. S. Ault and D. B. Olson, Effects of spatial grouping on the functional response of predators,, Theoret. Population Biol. 56 (1999), (1999), 65. Google Scholar 
[6] 
A. P. Gutierrez, The physiological basis of ratiodependent predatorprey theory: a metabolic pool model of Nicholson's blowflies as an example,, Ecology 73 (1992), (1992), 1552. Google Scholar 
[7] 
D. Henry, Geometric Theory of Semilinear Parabolic Equations,, Lecture Notes in Mathematics, (1993). Google Scholar 
[8] 
S. B. Hsu, T. W. Hwang and Y. Kuang, Global analysis of the MichaelisMententype ratiodependent predatorprey system,, J. Math. Biol. 42 (2001), (2001), 489. Google Scholar 
[9] 
S. B. Hsu, T. W. Hwang and Y. Kuang, Rich dynamics of a ratiodependent oneprey twopredators model,, J. Math. Biol. 43 (2001), (2001), 377. Google Scholar 
[10] 
S. B. Hsu, T. W. Hwang and Y. Kuang, A ratiodependent food chain model and its applications to biological control,, Math. Biosci. 181 (2003), (2003), 55. Google Scholar 
[11] 
Y. Kuang and E. Beretta, Global qualitative analysis of a ratiodependent predatorprey system,, {\em J. Math. Biol.} 36 (1998), (1998), 389. Google Scholar 
[12] 
Z. Lin and M. Pedersen, Stability in a diffusive foodchain model with MichaelisMenten functional response,, Nonlinear Anal. 57(2004) 421433., (2004), 421. Google Scholar 
[13] 
P. Y. H. Pang and M. X. Wang, Stragey and stationary pattern in a threespecies predatorprey model,, J. Differential Equations, (2004), 245. Google Scholar 
[14] 
P. Y. H. Pang and M. X. Wang, Qualitative analysis of a ratiodependent predatorprey system with diffusion,, Proc. Roy. Soc. Edinburgh Sect. A 133 (4) (2003), (2003), 919. Google Scholar 
[15] 
C. V. Pao, Quasisolutions and global attractor of reactiondiffusion systems,, Nonlinear Anal. 26(1996), (1996), 1889. Google Scholar 
[16] 
Y. Xiao and L. Chen, A ratiodependent predatorprey model with disease in the prey,, Appl. Maths. Comp. 131(2002), (2002), 397. Google Scholar 
show all references
References:
[1] 
R. Arditi and L. R. Ginzburg, Coupling in predatorprey dynamics: ratio dependence,, J. Theor. Biol. 139 (1989), (1989), 311. Google Scholar 
[2] 
R. Arditi, L. R. Ginzburg and H. R. Akcakaya, Variation in plankton densities among lakes: a case for ratiodependent models,, American Naturalist 138 (1991), (1991), 1287. Google Scholar 
[3] 
R. Arditi and H. Saiah, Empirical evidence of the role of heterogeneity in ratiodependent consumption,, Ecology 73 (1992), (1992), 1544. Google Scholar 
[4] 
R. S. Cantrell and C. Cosner, On the dynamics of predatorprey models with the BeddingtonDeAngelis functional response,, J. Math. Anal. Appl. 257 (2001), (2001), 206. Google Scholar 
[5] 
C. Cosner, D. L. DeAngelis, J. S. Ault and D. B. Olson, Effects of spatial grouping on the functional response of predators,, Theoret. Population Biol. 56 (1999), (1999), 65. Google Scholar 
[6] 
A. P. Gutierrez, The physiological basis of ratiodependent predatorprey theory: a metabolic pool model of Nicholson's blowflies as an example,, Ecology 73 (1992), (1992), 1552. Google Scholar 
[7] 
D. Henry, Geometric Theory of Semilinear Parabolic Equations,, Lecture Notes in Mathematics, (1993). Google Scholar 
[8] 
S. B. Hsu, T. W. Hwang and Y. Kuang, Global analysis of the MichaelisMententype ratiodependent predatorprey system,, J. Math. Biol. 42 (2001), (2001), 489. Google Scholar 
[9] 
S. B. Hsu, T. W. Hwang and Y. Kuang, Rich dynamics of a ratiodependent oneprey twopredators model,, J. Math. Biol. 43 (2001), (2001), 377. Google Scholar 
[10] 
S. B. Hsu, T. W. Hwang and Y. Kuang, A ratiodependent food chain model and its applications to biological control,, Math. Biosci. 181 (2003), (2003), 55. Google Scholar 
[11] 
Y. Kuang and E. Beretta, Global qualitative analysis of a ratiodependent predatorprey system,, {\em J. Math. Biol.} 36 (1998), (1998), 389. Google Scholar 
[12] 
Z. Lin and M. Pedersen, Stability in a diffusive foodchain model with MichaelisMenten functional response,, Nonlinear Anal. 57(2004) 421433., (2004), 421. Google Scholar 
[13] 
P. Y. H. Pang and M. X. Wang, Stragey and stationary pattern in a threespecies predatorprey model,, J. Differential Equations, (2004), 245. Google Scholar 
[14] 
P. Y. H. Pang and M. X. Wang, Qualitative analysis of a ratiodependent predatorprey system with diffusion,, Proc. Roy. Soc. Edinburgh Sect. A 133 (4) (2003), (2003), 919. Google Scholar 
[15] 
C. V. Pao, Quasisolutions and global attractor of reactiondiffusion systems,, Nonlinear Anal. 26(1996), (1996), 1889. Google Scholar 
[16] 
Y. Xiao and L. Chen, A ratiodependent predatorprey model with disease in the prey,, Appl. Maths. Comp. 131(2002), (2002), 397. Google Scholar 
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