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Volumn 155, Issue 2, 1999, Pages 368-404

Dynamics of a Periodically Pulsed Bio-reactor Model

Author keywords

Global attractivity; Positive periodic solutions; Principal eigenvalues; Uniform persistence

Indexed keywords


EID: 0033164394     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1998.3587     Document Type: Article
Times cited : (40)

References (36)
  • 1
    • 0000614595 scopus 로고
    • An application of the invariance principle to reaction-diffusion equations
    • Alikakos N. D. An application of the invariance principle to reaction-diffusion equations. J. Differential Equations. 33:1979;201-225.
    • (1979) J. Differential Equations , vol.33 , pp. 201-225
    • Alikakos, N.D.1
  • 2
    • 84967768783 scopus 로고
    • Quasilinear evolution equations and parabolic systems
    • Amann H. Quasilinear evolution equations and parabolic systems. Trans. Amer. Math. Soc. 293:1986;191-227.
    • (1986) Trans. Amer. Math. Soc. , vol.293 , pp. 191-227
    • Amann, H.1
  • 3
    • 0032201842 scopus 로고    scopus 로고
    • Effects of random motility on microbial growth and competition in a flow reactor
    • Ballyk M., Le D., Jones D. A., Smith H. L. Effects of random motility on microbial growth and competition in a flow reactor. SIAM J. Appl. Math. 59:1998;573-596.
    • (1998) SIAM J. Appl. Math. , vol.59 , pp. 573-596
    • Ballyk, M.1    Le, D.2    Jones, D.A.3    Smith, H.L.4
  • 4
    • 0000322496 scopus 로고
    • The chain recurrent set, attractors, and explosions
    • Block L., Franke J. E. The chain recurrent set, attractors, and explosions. Ergodic Theory Dynam. Systems. 5:1985;321-327.
    • (1985) Ergodic Theory Dynam. Systems , vol.5 , pp. 321-327
    • Block, L.1    Franke, J.E.2
  • 6
    • 0001283333 scopus 로고
    • Stability of fixed points for order-preserving discrete-time dynamical systems
    • Dancer E., Hess P. Stability of fixed points for order-preserving discrete-time dynamical systems. J. Reine Angew. Math. 419:1991;125-139.
    • (1991) J. Reine Angew. Math. , vol.419 , pp. 125-139
    • Dancer, E.1    Hess, P.2
  • 8
    • 0001572529 scopus 로고
    • Persistence in discrete semi-dynamical systems
    • Freedman H. I., So J. W.-H. Persistence in discrete semi-dynamical systems. SIAM J. Math. Anal. 20:1989;930-938.
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 930-938
    • Freedman, H.I.1    So, J.W.-H.2
  • 12
    • 0001641843 scopus 로고
    • On an abstract competition model and applications
    • Hess P., Lazer A. C. On an abstract competition model and applications. Nonlinear Anal. 16:1991;917-940.
    • (1991) Nonlinear Anal. , vol.16 , pp. 917-940
    • Hess, P.1    Lazer, A.C.2
  • 13
    • 84966222841 scopus 로고
    • Uniform persistence and repellors for maps
    • Hofbauer J., So J. W.-H. Uniform persistence and repellors for maps. Proc. Amer. Math. Soc. 107:1989;1137-1142.
    • (1989) Proc. Amer. Math. Soc. , vol.107 , pp. 1137-1142
    • Hofbauer, J.1    So, J.W.-H.2
  • 14
    • 0026616222 scopus 로고
    • Permanence and the dynamics of biological systems
    • Hutson V., Schmitt K. Permanence and the dynamics of biological systems. Math. Biosci. 111:1992;1-71.
    • (1992) Math. Biosci. , vol.111 , pp. 1-71
    • Hutson, V.1    Schmitt, K.2
  • 16
    • 21444453892 scopus 로고    scopus 로고
    • Competitive exclusion and coexistence for competitive systems on ordered Banach spaces
    • Hsu S. B., Smith H. L., Waltman P. Competitive exclusion and coexistence for competitive systems on ordered Banach spaces. Trans. Amer. Math. Soc. 348:1996;4083-4094.
    • (1996) Trans. Amer. Math. Soc. , vol.348 , pp. 4083-4094
    • Hsu, S.B.1    Smith, H.L.2    Waltman, P.3
  • 17
    • 0000802631 scopus 로고
    • Persistence in infinite-dimensional systems
    • Hale J. K., Waltman P. Persistence in infinite-dimensional systems. SIAM J. Math. Anal. 20:1989;388-395.
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 388-395
    • Hale, J.K.1    Waltman, P.2
  • 18
    • 0026707308 scopus 로고
    • The growth of pure and simple microbial competitors in a moving distributed medium
    • Kung C.-M., Baltzis B. The growth of pure and simple microbial competitors in a moving distributed medium. Math. Biosci. 111:1992;295-313.
    • (1992) Math. Biosci. , vol.111 , pp. 295-313
    • Kung, C.-M.1    Baltzis, B.2
  • 20
    • 0030239605 scopus 로고    scopus 로고
    • A parabolic system modeling microbial competition in an unmixed bio-reactor
    • Le D., Smith H. L. A parabolic system modeling microbial competition in an unmixed bio-reactor. J. Differential Equations. 160:1996;59-91.
    • (1996) J. Differential Equations , vol.160 , pp. 59-91
    • Le, D.1    Smith, H.L.2
  • 21
    • 0009418458 scopus 로고
    • Global stability of the endemic equilibrium and uniform persistence in epidemic models with subpopulations
    • Lin X., So J. W.-H. Global stability of the endemic equilibrium and uniform persistence in epidemic models with subpopulations. J. Austral. Math. Soc. Ser. B. 34:1993;282-295.
    • (1993) J. Austral. Math. Soc. Ser. B , vol.34 , pp. 282-295
    • Lin, X.1    So, J.W.-H.2
  • 22
    • 0001435105 scopus 로고    scopus 로고
    • Growth in the unstirred chemostat with different diffusion rates
    • Le D., Smith H. L., Waltman P. Growth in the unstirred chemostat with different diffusion rates. Fields Institute Communications. 21:1999;131-142.
    • (1999) Fields Institute Communications , vol.21 , pp. 131-142
    • Le, D.1    Smith, H.L.2    Waltman, P.3
  • 23
    • 84966246501 scopus 로고
    • Abstract functional differential equations and reaction-diffusion systems
    • Martin R. H., Smith H. L. Abstract functional differential equations and reaction-diffusion systems. Trans. Amer. Math. Soc. 321:1990;1-44.
    • (1990) Trans. Amer. Math. Soc. , vol.321 , pp. 1-44
    • Martin, R.H.1    Smith, H.L.2
  • 24
    • 0000703838 scopus 로고
    • Asymptotically autonomous semiflows: Chain recurrence and Liapunov functions
    • Mischaikow K., Smith H. L., Thieme H. R. Asymptotically autonomous semiflows: Chain recurrence and Liapunov functions. Trans. Amer. Math. Soc. 347:1995;1669-1685.
    • (1995) Trans. Amer. Math. Soc. , vol.347 , pp. 1669-1685
    • Mischaikow, K.1    Smith, H.L.2    Thieme, H.R.3
  • 27
    • 85034188422 scopus 로고    scopus 로고
    • Competition in a chemostat with wall growth
    • to appear
    • S. Pilyugin, and, P. Waltman, Competition in a chemostat with wall growth, SIAM J. Appl. Math, to appear.
    • SIAM J. Appl. Math
    • Pilyugin, S.1    Waltman, P.2
  • 28
    • 0001570568 scopus 로고
    • Stability theorems and hyperbolicity in dynamical systems
    • Robinson C. Stability theorems and hyperbolicity in dynamical systems. Rocky Mountain J. Math. 7:1977;425-437.
    • (1977) Rocky Mountain J. Math. , vol.7 , pp. 425-437
    • Robinson, C.1
  • 31
    • 22444452981 scopus 로고    scopus 로고
    • Perturbation of a globally stable steady state
    • Smith H. L., Waltman P. Perturbation of a globally stable steady state. Proc. Amer. Math. Soc. 127:1999;447-453.
    • (1999) Proc. Amer. Math. Soc. , vol.127 , pp. 447-453
    • Smith, H.L.1    Waltman, P.2
  • 32
    • 0039591930 scopus 로고
    • Persistence under relaxed point-dissipativity (with application to an epidemic model)
    • Thieme H. R. Persistence under relaxed point-dissipativity (with application to an epidemic model). SIAM J. Math. Anal. 24:1993;407-435.
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 407-435
    • Thieme, H.R.1
  • 34
    • 0000313693 scopus 로고
    • Uniform persistence and periodic coexistence states in infinite-dimensional periodic semiflows with applications
    • Zhao X.-Q. Uniform persistence and periodic coexistence states in infinite-dimensional periodic semiflows with applications. Canad. Appl. Math. Quart. 3:1995;473-495.
    • (1995) Canad. Appl. Math. Quart. , vol.3 , pp. 473-495
    • Zhao, X.-Q.1
  • 35
    • 0000224082 scopus 로고    scopus 로고
    • Global attractivity and stability in some monotone discrete dynamical systems
    • Zhao X.-Q. Global attractivity and stability in some monotone discrete dynamical systems. Bull. Austral. Math. Soc. 53:1996;305-324.
    • (1996) Bull. Austral. Math. Soc. , vol.53 , pp. 305-324
    • Zhao, X.-Q.1
  • 36
    • 0001985801 scopus 로고    scopus 로고
    • Asymptotic behavior for asymptotically periodic semiflows with applications
    • Zhao X.-Q. Asymptotic behavior for asymptotically periodic semiflows with applications. Comm. Appl. Nonlinear Anal. 3:1996;43-66.
    • (1996) Comm. Appl. Nonlinear Anal. , vol.3 , pp. 43-66
    • Zhao, X.-Q.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.