Dynamics of a plasmid chemostat model with periodic nutrient input and delayed nutrient recycling

Nonlinear Analysis: Real World Applications

Volumn 13, Issue 5, 2012, Pages 2104-2119

  Yuan, Sanling ^a   Zhang, Tonghua ^b  

^a UNIVERSITY OF SHANGHAI FOR SCIENCE AND TECHNOLOGY   (China)

^b SWINBURNE UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

Chemostat; Nutrient recycling; Periodic solution; Permanence; Plasmid bearing

Indexed keywords

BACTERIAL DECOMPOSITION; CHEMOSTAT MODELS; DELAYED NUTRIENT RECYCLING; DISTRIBUTED DELAYS; GLOBAL STABILITY; INTRASPECIFIC COMPETITION; NUTRIENT RECYCLING; PERIODIC SOLUTION; PERMANENCE; PLASMID-BEARING; POSITIVE PERIODIC SOLUTION; SUFFICIENT CONDITIONS; THEORETICAL RESULT;

CHEMOSTATS; NUTRIENTS; PROBLEM SOLVING; RECYCLING;

DNA;

EID: 84863411114     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2012.01.006     Document Type: Article

References (52)

1. H. Smith, P. Waltman, The Theory of the Chemostat, Cambridge University, Cambridge, UK, 1995.
2. P.A. Taylor, and J.L. Williams Theoretical studies on the coexistence of competing species under continuous-flow conditions Can. J. Microbiol. 21 1975 90 98
3. A.G. Frederickson, and G. Stephanopoulis Microbial competition Science 213 1981 972 979
4. H.L. Smith Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems Math. Surv. and Monographs vol. 41 1995 AMS Providence, RI
5. D.F. Ryder, and D. DiBiasio An operational strategy for unstable recombinant DNA cultures Biotechnology and Bioengineering 26 1984 942 957
6. G. Stephanopoulis, and G. Lapidus Chemostat dynamics of plasmid-bearing plasmid-free mixed recombinant cultures Chem. Eng. Sci. 43 1988 49 57
7. S.B. Hsu, P. Waltman, and G.S.K. Wolkowicz Global analysis of a model of plasmid-bearing, plasmid-free competition in a chemostat J. Math. Biol. 32 1994 731 742
8. S.B. Hsu, and P. Waltman Competition between plasmid-bearing and plasmid-free organisms in selective media Chem. Eng. Sci. 52 1997 23 35
9. S.B. Hsu, T.K. Luo, and P. Waltman Competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitor J. Math. Biol. 34 1995 225 238
10. S.B. Hsu, and P. Waltman A model of the effect of anti-competitor toxins on plasmid-bearing, plasmid-free organisms Taiwannese J. Math. 6 2002 135 155
11. S.B. Hsu, and P. Waltman A survey of mathematical models of competition with an inhibitor Math. Biosci. 187 2004 53 91
12. S.B. Hsu, and C.C. Li A discrete-delayed model with plasmid-bearing, plalmid-free competition in a chemostat Discrete Contin. Dyn. Syst. Ser. B 5 2005 699 718
13. T.K. Luo, and S.B. Hsu Global analysis of a model of plasmid-bearing, plasmid-free competition in a chemostat with inhibitions J. Math. Biol. 34 1995 41 76
14. Z. Lu, and K.P. Hadeler Model of plasmid-bearing, plasmid-free competition in the chemostat with nutrient recycling and an inhibitor Math. Biosci. 148 1998 147 159
15. S. Ai Periodic solution in a chemostat of competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitor J. Math. Biol. 42 2001 71 94
16. A. Ajbar Classification of static and dynamic behavior in chemostat for plasmid-bearing, plasmid-free mixed recombinant culture Chem. Eng. Commun. 189 2002 1130 1154
17. K. Alhumaizi, A. Alwan, and A. Ajbar Competition of plasmid-bearing and plasmid-free organisms in a chemostat: a study of bifurcation phenomena Math. Comput. Modelling 44 2006 342 367
18. J. Wu, H. Nie, and G.S.K. Wolkowicz The effect of inhibitor on the plasmid-bearing and plasmid-free model in the unstirred chemostat SIAM J. Math. Anal. 38 2007 1860 1885
19. H. Nie, and J. Wu Coexistence of an unstirred chemostat model with BeddingtonDeAngelis functional response and inhibitor Nonlinear Anal. RWA 11 2010 3639 3652
20. P. Kumar, and S. Ghosh Population dynamics model for plasmid bearing and plasmid lacking cells for streptokinase production in continuous flow stirred tank bioreactor Int. J. Eng. Sci. Technol. 2 2010 118 127
21. M.M.E. Abashar, and S.S.E.H. Elnashaie Dynamic and chaotic behavior of periodically forced fermentors for bioethanol production Chem. Eng. Sci. 65 2010 4894 4905
22. Z. Xiang, and X. Song A model of competition between plasmid-bearing and plasmid-free organisms in a chemostat with periodic input Chaos Solitons Fractals 32 2007 1419 1428
23. A. Gaki, A. Theodorou, D.V. Vayenas, and S. Pavlou Complex dynamics of microbial competition in the gradostat J. Biotechnol. 139 2009 38 46
24. M. Popov, S. Petrov, G. Nacheva, I. Ivanov, and U. Reichl Effects of a recombinant gene expression on ColE1-like plasmid segregation in Escherichia coli BMC Biotechnol. 11 2011 Art. no. 18
25. S. Sinha, O.P. Misra, and J. Dhar A two species competition model under the simultaneous effect of toxicant and disease Nonlinear Anal. RWA 11 2010 1131 1142
26. G. Robledo, F. Grognard, and J.-L. Gouz Global stability for a model of competition in the chemostat with microbial inputs Nonlinear Anal. RWA 13 2012 582 598
27. H. Zhang, P. Georgescu, J.J. Nieto, and L. Chen Impulsive perturbation and bifurcation of solutions for a model of chemostat with variable yield Appl. Math. Mech. 30 2009 933 944 (English Edition)
28. X. Meng, Q. Gao, and Z. Li The effects of delayed growth response on the dynamic behaviors of the Monod type chemostat model with impulsive input nutrient concentration Nonlinear Anal. RWA 11 2010 4476 4486
29. S. Yuan, D. Xiao, and M. Han Competition between plasmid-bearing and plasmid-free organisms in a chemostat with nutrient recycling and an inhibitor Math. Biosci. 202 2006 1 28
30. S. Yuan, W. Zhang, and Y. Zhao Bifurcation analysis of a model of plasmid-bearing, plasmid-free competition in a pulsed chemostat with an internal inhibitor IMA J. Appl. Math. 76 2011 277 297
31. S. Yuan, Y. Song, and J. Li Oscillations in a plasmid turbidostat model with delayed feedback control Discrete Contin. Dyn. Syst. Ser. B 15 2011 809 914
32. S. Yuan, Y. Zhao, and A. Xiao Competition between plasmid-bearing and plasmid-free organisms in a chemostat with pulsed input and washout Math. Probl. Eng. 2009 Art. no. 204632
33. E. Beretta, G.I. Bischi, and F. Solimano Stability in chemostat equations with delayed nutrient recycling J. Math. Biol. 28 1990 99 111
34. H.I. Freedman, and Y. Xu Models of competition in the chemostat with instantaneous and delayed nutrient recycling J. Math. Biol. 31 1993 513 527
35. E. Beretta, and Y. Takeuchi Global stability for chemostat equations with delayed nutrient recycling Nonlinear World 1 1994 291 306
36. G.J. Butler, and G.S.K. Wolkowicz A mathematical model of the chemostat with a general class of functions describing nutrient uptake SIAM J. Appl. Math. 45 1985 138 151
37. S.B. Hsu Limiting behavior for competing species SIAM J. Appl. Math. 34 1978 760 763
38. S. Yuan, and M. Han Bifurcation analysis of a chemostat model with two distributed delays Chaos Solitons Fractals 20 2004 995 1004
39. S. Yuan, Y. Song, and M. Han Direction and stability of bifurcating periodic solutions of a chemostat model with two distributed delays Chaos Solitons Fractals 21 2004 1109 1123
40. S. Ruan, and X.-Z. He Global stability in chemostat-type competition models with nutrient recycling SIAM J. Appl. Math. 58 1 1998 170 192
41. S. Yuan, W. Zhang, and M. Han Global asymptotic behavior in chemostat-type competition models with delay Nonlinear Anal. RWA 10 2009 1305 1320
42. R.S. Cantrell, C. Cosner, and S. Ruan Intraspecific interference and consumer-resource dynamics Discrete Contin. Dyn. Syst. 4 2004 527 546
43. S. Ruan Persistence and coexistence in zooplankton-phytoplankton-nutrient models with instantaneous nutrient recycling J. Math. Biol. 31 1993 633 654
44. S.B. Hsu A competition model for a seasonally flluctuating nutrient J. Math. Biol. 9 1980 115 132
45. X. Meng, Z. Li, and J.J. Nieto Dynamic analysis of MichaelisMenten chemostat-type competition models with time delay and pulse in a polluted environment J. Math. Chem. 47 2010 123 144
46. Z. Zhao, T. Wang, and L. Chen Dynamic analysis of a turbidostat model with the feedback control Commun. Nonlinear Sci. Numer. Simul. 15 2010 1028 1035
47. Z. Zhao, L. Yang, and L. Chen Impulsive state feedback control of the microorganism culture in a turbidostat J. Math. Chem. 47 2010 1224 1239
48. N. MacDonald Time Lags in Biological Models 1978 Springer Heidelberg
49. K. Sawano Some considerations on the fundemental theorems for functional differential equations with infinite delay Funkcial. Ekvac. 25 1982 97 104
50. T.A. Burton, D.P. Dwiggins, and Y. Feng Periodic solutions of functional differential equations with infinite delay J. Lond. Math. Soc. 2 1989 81 88
51. K. Gopalsamy Stability and Oscillations in Delay Differential Equations of Population Dynamics 1992 Kluwer Academic Publishers Dordrecht, The Netherlands
52. S.B. Hsu, and Y.H. Tzeng Plasmid-bearing, plasmid-free organisms competing for two complementary nutrients in a chemostat Math. Biosci. 179 2002 183 206