Bifurcation from a double eigenvalue in the unstirred chemostat

References

• Schuler , ML and Kargi , F . 1992 . Bioprocess Engineering Basic Concepts , Englewood Cliffs, NJ : Prentice-Hall .
   Google Scholar
• Freter , R . 1983 . “ Mechanisms that control the microflora in the large intestine ” . In Human Intestinal Microflora in Health and Diseases , Edited by: Hentges , DJ . 33 – 54 . New York : Academic Press .
   Google Scholar
• Smith , HL and Waltman , P . 1995 . The Theory of the Chemostat: Dynamics of Microbial Competition , Cambridge : Cambridge University .
   Google Scholar
• So , J-H and Waltman , P . 1989 . A nonlinear boundary value problem arising from competition in the chemostat . Appl. Math. Comput. , 32 : 169 – 183 .
   Web of Science ®Google Scholar
• Hsu , SB and Waltman , P . 1993 . On a system of reaction-diffusion equations arising from competition in an unstirred Chemostat . SIAM J. Appl. Math. , 53 : 1026 – 1044 .
   Web of Science ®Google Scholar
• Wu , JH . 2000 . Global bifurcation of coexistence state for the competition model in the chemostat . Nonlinear Anal. , 39 : 817 – 835 .
   Web of Science ®Google Scholar
• Dung , L and Smith , HL . 1996 . A parabolic system modelling microbial competition in an unmixed bio-reactor . J. Differ. Eqns , 130 : 59 – 91 .
   Web of Science ®Google Scholar
• Wu , JH and Wolkowicz , GSK . 2001 . A system of resource-based growth models with two resources in the unstirred chemostat . J. Differ. Eqns , 172 : 300 – 332 .
   Web of Science ®Google Scholar
• Wu , JH , Nie , H and Wolkowicz , GSK . 2004 . A mathematical model of competition for two essential resources in the unstirred chemostat . SIAM J. Appl. Math. , 65 : 209 – 229 .
   Web of Science ®Google Scholar
• Nie , H and Wu , JH . 2006 . A system of reaction-diffusion equations in the unstirred chemostat with an inhibitor . International J. Bifurcation and Chaos , 16 ( 4 ) : 989 – 1009 .
   Web of Science ®Google Scholar
• Nie , H and Wu , JH . 2007 . Asymptotic behavior of an unstirred chemostat model with internal inhibitor . J. Math. Anal. Appl. , 334 ( 2 ) : 889 – 908 .
   Web of Science ®Google Scholar
• Wu , JH , Nie , H and Wolkowicz , GSK . 2007 . The effect of inhibitor on the plasmid-bearing and plasmid-free model in the unstirred chemostat . SIAM J. Math. Anal. , 38 : 1860 – 1885 .
   Web of Science ®Google Scholar
• Ye , QX and Li , ZY . 1990 . Introduction to Reaction-Diffusion Equations , Beijing : Science Press . (in Chinese)
   Google Scholar
• Yamada , Y . 1990 . Stability of steady states for prey-predator diffusion equations with homogeneous Dirichlet conditions . SIAM J. Math. Anal. , 21 : 327 – 345 .
   Web of Science ®Google Scholar
• Ito , M . 1984 . Global aspect of steady-states for competitive-diffuse systems with homogeneous Dirichlet conditions . Phys. D , 14 : 1 – 28 .
   Web of Science ®Google Scholar
• Kato , T . 1980 . Perturbation Theory for Linear Operators , 2nd , Berlin , , New York : Springer-Verlag .
   Google Scholar
• Crandall , MG and Rabinowitz , PH . 1971 . Bifurcation from simple eigenvalues . J. Funct. Anal. , 8 : 321 – 340 .
   Google Scholar