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Volumn 367, Issue 1908, 2009, Pages 4685-4697

Study of a virus-bacteria interaction model in a chemostat: application of geometrical singular perturbation theory

Author keywords

Invariant manifold; Reduction; Singular perturbation; Virus bacteria interaction

Indexed keywords

BACTERIA; BACTERIOLOGY; CHEMOSTATS; NONLINEAR CONTROL SYSTEMS; PHASE SPACE METHODS; VIRUSES;

EID: 73349135343     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2009.0132     Document Type: Article
Times cited : (9)

References (29)
  • 1
    • 0032006632 scopus 로고    scopus 로고
    • Aggregation and emergence in systems of ordinary differential equations
    • doi:10.1016/S0895-7177(98)00002-8
    • Auger, P. & Poggiale, J. C. 1998 Aggregation and emergence in systems of ordinary differential equations. Math. Comput. Model. 27, 1-21. (doi:10.1016/S0895-7177(98)00002-8)
    • (1998) Math. Comput. Model , vol.27 , pp. 1-21
    • Auger, P.1    Poggiale, J.C.2
  • 2
    • 0001920442 scopus 로고
    • Complex ecological models with simple dynamics from individuals to populations
    • doi:10.1007/BF00709485
    • Auger, P. & Roussarie, R. 1994 Complex ecological models with simple dynamics from individuals to populations. Acta Biotheor. 42, 111-136. (doi:10.1007/BF00709485)
    • (1994) Acta Biotheor , vol.42 , pp. 111-136
    • Auger, P.1    Roussarie, R.2
  • 3
    • 44149116706 scopus 로고    scopus 로고
    • Aggregation methods in dynamical systems and applications in population and community dynamics
    • doi:10.016/j.plrev.2008.02.001
    • Auger, P., Bravo de la Parra, R., Poggiale, J.-C., Sanchez, E. & Sanz, L. 2008a Aggregation methods in dynamical systems and applications in population and community dynamics. Phys. Life Rev. 5, 79-105. (doi:10.016/j.plrev.2008.02.001)
    • (2008) Phys. Life Rev , vol.5 , pp. 79-105
    • Auger, P.1    Bravo de la Parra, R.2    Poggiale, J.-C.3    Sanchez, E.4    Sanz, L.5
  • 4
    • 44149126797 scopus 로고    scopus 로고
    • Aggregation of variables and applications to population dynamics
    • Structured population models in biology and epidemiology eds P. Magal & S. Ruan, Berlin, Germany: Springer
    • Auger, P., Bravo de la Parra, R., Poggiale, J.-C., Sanchez, E. & Nguyen-Huu, T. 2008b Aggregation of variables and applications to population dynamics. in Structured population models in biology and epidemiology (eds P. Magal & S. Ruan). Lecture Notes in Mathematics, vol. 1936, pp. 209-224. Berlin, Germany: Springer.
    • (2008) Lecture Notes in Mathematics , vol.1936 , pp. 209-224
    • Auger, P.1    Bravo de la Parra, R.2    Poggiale, J.-C.3    Sanchez, E.4    Nguyen-Huu, T.5
  • 5
    • 0031802262 scopus 로고    scopus 로고
    • Modeling and analysis of a marine bacteriophage infection
    • doi:10.1016/S0025-5564(97)10015-3
    • Beretta, E. & Kuang, Y. 1998 Modeling and analysis of a marine bacteriophage infection. Math. Biosci. 149, 57-76. (doi:10.1016/S0025-5564(97)10015-3)
    • (1998) Math. Biosci , vol.149 , pp. 57-76
    • Beretta, E.1    Kuang, Y.2
  • 6
    • 0024475207 scopus 로고
    • High abundances of viruses found in aquatic environments
    • doi:10.1038/340467a0
    • Bergh, O., Borsheim, K. Y., Bratbak, G. & Heldal, M. 1989 High abundances of viruses found in aquatic environments. Nature 340, 467-468. (doi:10.1038/340467a0)
    • (1989) Nature , vol.340 , pp. 467-468
    • Bergh, O.1    Borsheim, K.Y.2    Bratbak, G.3    Heldal, M.4
  • 7
    • 0036176248 scopus 로고    scopus 로고
    • On the stability properties of a stochastic model for phage-bacteria interaction in open marine environment
    • doi:10.1016/S0025-5564(01)00089-x
    • Carletti, M. 2002 On the stability properties of a stochastic model for phage-bacteria interaction in open marine environment. Math. Biosci. 175, 117-131. (doi:10.1016/S0025-5564(01)00089-x)
    • (2002) Math. Biosci , vol.175 , pp. 117-131
    • Carletti, M.1
  • 8
    • 0347600676 scopus 로고    scopus 로고
    • Numerical simulation of stochastic ordinary differential equations in biomathematical modelling
    • doi:10.1016/j.matcom.2003.09. 002
    • Carletti, M., Burrage, K. & Burrage, P. M. 2004 Numerical simulation of stochastic ordinary differential equations in biomathematical modelling. Math. Comput. Simul. 64, 271-277. (doi:10.1016/j.matcom.2003.09. 002)
    • (2004) Math. Comput. Simul , vol.64 , pp. 271-277
    • Carletti, M.1    Burrage, K.2    Burrage, P.M.3
  • 9
    • 0036710119 scopus 로고    scopus 로고
    • Food chain chaos due to Shilnikov's orbit
    • doi:10.1063/1.1482255
    • Deng, B. & Hines, G. 2002 Food chain chaos due to Shilnikov's orbit. Chaos 12, 533-538. (doi:10.1063/1.1482255)
    • (2002) Chaos , vol.12 , pp. 533-538
    • Deng, B.1    Hines, G.2
  • 10
    • 0001356311 scopus 로고
    • Persistence and smoothness of invariant manifolds for flows
    • doi:10.1512/iumj.1971. 21.21017
    • Fenichel, N. 1971 Persistence and smoothness of invariant manifolds for flows. Indiana Univ. Math. J. 21, 193-226. (doi:10.1512/iumj.1971. 21.21017)
    • (1971) Indiana Univ. Math. J , vol.21 , pp. 193-226
    • Fenichel, N.1
  • 11
    • 34250627892 scopus 로고
    • Geometric singular perturbation theory for ordinary differential equations
    • doi:10.1016/0022-0396(79)90152-9
    • Fenichel, N. 1979 Geometric singular perturbation theory for ordinary differential equations. J. Differ. Equat. 31, 53-98. (doi:10.1016/0022-0396(79)90152-9)
    • (1979) J. Differ. Equat , vol.31 , pp. 53-98
    • Fenichel, N.1
  • 12
    • 0033542481 scopus 로고    scopus 로고
    • Marine viruses and their biogeochemical and ecological effects
    • doi:10.11038/21119
    • Fuhrman, J. A. 1999 Marine viruses and their biogeochemical and ecological effects. Nature 399, 541-548. (doi:10.11038/21119)
    • (1999) Nature , vol.399 , pp. 541-548
    • Fuhrman, J.A.1
  • 13
    • 0002316532 scopus 로고
    • Geometric singular perturbation theory
    • Dynamical systems ed. R. Johnson, Berlin, Germany: Springer
    • Jones, C. K. R. T. 1994 Geometric singular perturbation theory. In Dynamical systems (ed. R. Johnson). Lecture Notes in Mathematics, vol. 1609, pp. 44-118. Berlin, Germany: Springer.
    • (1994) Lecture Notes in Mathematics , vol.1609 , pp. 44-118
    • Jones, C.K.R.T.1
  • 14
    • 85020784492 scopus 로고    scopus 로고
    • Jones, C. K. R. T. & Khibnik, A. I. (eds) 2000 Geometric singular perturbation theory beyond normal hyperbolicity. In Multiple-time-scale dynamical systems. The IMA in Mathematics and its Applications, 122. New York, NY: Springer.
    • Jones, C. K. R. T. & Khibnik, A. I. (eds) 2000 Geometric singular perturbation theory beyond normal hyperbolicity. In Multiple-time-scale dynamical systems. The IMA Volumes in Mathematics and its Applications, vol. 122. New York, NY: Springer.
  • 15
    • 0032005158 scopus 로고    scopus 로고
    • Aggregation methods in food chains
    • doi:10.1016/S0895-7177(98)00011-9
    • Kooi, B. W., Poggiale, J. C. & Auger, P. M. 1998 Aggregation methods in food chains. Math. Comput. Model. 27, 109-120. (doi:10.1016/S0895-7177(98)00011-9)
    • (1998) Math. Comput. Model , vol.27 , pp. 109-120
    • Kooi, B.W.1    Poggiale, J.C.2    Auger, P.M.3
  • 16
    • 0038205228 scopus 로고
    • Asymptotically autonomous differential systems
    • ed. S. Lefschetz, Princeton, NJ: Princeton University Press
    • Markus, L. 1956 Asymptotically autonomous differential systems. In Contributions to the theory of nonlinear oscillations III (ed. S. Lefschetz). Princeton, NJ: Princeton University Press.
    • (1956) Contributions to the theory of nonlinear oscillations III
    • Markus, L.1
  • 17
    • 0033784827 scopus 로고    scopus 로고
    • Bacterial growth rate and marine virus-host dynamics
    • doi:10.1007/s002480000050
    • Middelboe, M. 2000 Bacterial growth rate and marine virus-host dynamics. Microb. Ecol. 40, 114-124. (doi:10.1007/s002480000050)
    • (2000) Microb. Ecol , vol.40 , pp. 114-124
    • Middelboe, M.1
  • 18
    • 0035211598 scopus 로고    scopus 로고
    • Effects of bacteriophages on the population dynamics of four strains of pelagic marine bacteria
    • doi:10.1007/s00248-001-0012- 1
    • Middelboe, M., Hagström, A., Blackburn, N., Sinn, B., Fischer, U., Borch, N. H., Pinhassi, J., Simu, K. & Lorenz, M. G. 2001 Effects of bacteriophages on the population dynamics of four strains of pelagic marine bacteria. Microb. Ecol. 42, 395-406. (doi:10.1007/s00248-001-0012- 1)
    • (2001) Microb. Ecol , vol.42 , pp. 395-406
    • Middelboe, M.1    Hagström, A.2    Blackburn, N.3    Sinn, B.4    Fischer, U.5    Borch, N.H.6    Pinhassi, J.7    Simu, K.8    Lorenz, M.G.9
  • 19
    • 0141788404 scopus 로고    scopus 로고
    • Virus-induced transfer of organic carbon between marine bacteria in a model community
    • doi:10.3354/ame033001
    • Middelboe, M., Riemann, L., Steward, G. F., Hansen, V. & Nybroe, O. 2003 Virus-induced transfer of organic carbon between marine bacteria in a model community. Aquat. Microb. Ecol. 33, 1-10. (doi:10.3354/ame033001)
    • (2003) Aquat. Microb. Ecol , vol.33 , pp. 1-10
    • Middelboe, M.1    Riemann, L.2    Steward, G.F.3    Hansen, V.4    Nybroe, O.5
  • 20
    • 0027072404 scopus 로고
    • Low- and high-frequency oscillations in three-dimensional food chain systems
    • doi:10.1137/0152097
    • Muratori, S. & Rinaldi, S. 1992 Low- and high-frequency oscillations in three-dimensional food chain systems. SIAM J. Appl. Math. 52, 1688-1706. (doi:10.1137/0152097)
    • (1992) SIAM J. Appl. Math , vol.52 , pp. 1688-1706
    • Muratori, S.1    Rinaldi, S.2
  • 21
    • 0025198355 scopus 로고
    • Viral mortality of marine bacteria and cyanobacteria
    • doi:10.1038/343060a0
    • Proctor, L. M. & Fuhrman, J. A. 1990 Viral mortality of marine bacteria and cyanobacteria. Nature 343, 60-62. (doi:10.1038/343060a0)
    • (1990) Nature , vol.343 , pp. 60-62
    • Proctor, L.M.1    Fuhrman, J.A.2
  • 22
    • 84974487746 scopus 로고
    • Invariant manifolds in singular perturbations problems for ordinary differential equations
    • Sakamoto, K. 1990 Invariant manifolds in singular perturbations problems for ordinary differential equations. Proc. R. Soc. Edinb. 116A, 45-78.
    • (1990) Proc. R. Soc. Edinb , vol.116 A , pp. 45-78
    • Sakamoto, K.1
  • 23
    • 25144506135 scopus 로고    scopus 로고
    • Viruses in the sea
    • doi:10.1038/nature04160
    • Suttle, C. A. 2005 Viruses in the sea. Nature 437, 356-361. (doi:10.1038/nature04160)
    • (2005) Nature , vol.437 , pp. 356-361
    • Suttle, C.A.1
  • 24
    • 77952672921 scopus 로고
    • Convergence results and a Poincaré-Bendixon trichotomy for asymptotically autonomous differential equations
    • doi:10.1007/BF00173267
    • Thieme, H. R. 1992 Convergence results and a Poincaré-Bendixon trichotomy for asymptotically autonomous differential equations. J. Math. Biol. 30, 755-763. (doi:10.1007/BF00173267)
    • (1992) J. Math. Biol , vol.30 , pp. 755-763
    • Thieme, H.R.1
  • 25
    • 84881166951 scopus 로고
    • Asymptotically autonomous differential equations in the plane
    • doi:10.1216/rmjm/118l072470
    • Thieme, H. R. 1994a Asymptotically autonomous differential equations in the plane. Rocky Mountain J. Math. 24, 351-380. (doi:10.1216/rmjm/118l072470)
    • (1994) Rocky Mountain J. Math , vol.24 , pp. 351-380
    • Thieme, H.R.1
  • 26
    • 33746945861 scopus 로고
    • Asymptotically autonomous differential equations in the plane II. Stricter Poincare-Bendixon results
    • Thieme, H. R. 1994b Asymptotically autonomous differential equations in the plane II. Stricter Poincare-Bendixon results. Differ. Integr. Equat. 7, 1625-1640.
    • (1994) Differ. Integr. Equat , vol.7 , pp. 1625-1640
    • Thieme, H.R.1
  • 27
    • 0002058563 scopus 로고    scopus 로고
    • Theoretical models for the control of bacterial growth rate, abundance, diversity and carbon demand
    • doi:10.3354/ame013019
    • Thingstad, T. F. & Lignell, R. 1997 Theoretical models for the control of bacterial growth rate, abundance, diversity and carbon demand. Aquat. Microb. Ecol. 13, 19-27. (doi:10.3354/ame013019)
    • (1997) Aquat. Microb. Ecol , vol.13 , pp. 19-27
    • Thingstad, T.F.1    Lignell, R.2
  • 28
    • 0003238449 scopus 로고
    • Normally hyperbolic invariant manifolds in dynamical systems
    • New York, NY: Springer
    • Wiggins, S. 1994 Normally hyperbolic invariant manifolds in dynamical systems. Applied Mathematical Sciences, vol. 105. New York, NY: Springer.
    • (1994) Applied Mathematical Sciences , vol.105
    • Wiggins, S.1
  • 29
    • 0032858844 scopus 로고    scopus 로고
    • Viruses and nutrient cycles in the sea
    • doi:10.2307/1313569
    • Wilhelm, S. W. & Suttle, C. A. 1999 Viruses and nutrient cycles in the sea. Bioscience 49, 781-788. (doi:10.2307/1313569)
    • (1999) Bioscience , vol.49 , pp. 781-788
    • Wilhelm, S.W.1    Suttle, C.A.2


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