메뉴 건너뛰기




Volumn 58, Issue 3, 2009, Pages 525-538

Periodic solution of a turbidostat model with impulsive state feedback control

Author keywords

Globally asymptotical stability; Impulsive effect; Periodic solution; State feedback control; Turbidostat

Indexed keywords

ASYMPTOTICAL STABILITY; CONTROL MEASURES; EXISTENCE AND STABILITY; GLOBAL ASYMPTOTICAL STABILITY; IMPULSIVE EFFECTS; PERIODIC SOLUTION; SUFFICIENT CONDITIONS;

EID: 70450270997     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-009-9498-8     Document Type: Article
Times cited : (28)

References (25)
  • 1
    • 0001188059 scopus 로고
    • Competitive exclusion
    • 10.1086/283553 596657
    • R.A. Armstrong R. McGehee 1980 Competitive exclusion Am. Nat. 115 151 170 10.1086/283553 596657
    • (1980) Am. Nat. , vol.115 , pp. 151-170
    • Armstrong, R.A.1    McGehee, R.2
  • 2
    • 0022012911 scopus 로고
    • A mathematical model of the chemostat with a general class of functions describing nutrient uptake
    • 0569.92020 10.1137/0145006 775486
    • G.J. Butler G.S.K. Wolkowicz 1985 A mathematical model of the chemostat with a general class of functions describing nutrient uptake SIAM J. Appl. Math. 45 138 151 0569.92020 10.1137/0145006 775486
    • (1985) SIAM J. Appl. Math. , vol.45 , pp. 138-151
    • Butler, G.J.1    Wolkowicz, G.S.K.2
  • 3
    • 0041758422 scopus 로고    scopus 로고
    • Feedback control for chemostat models
    • DOI 10.1007/s00285-002-0170-x
    • P. De Leenheer H.L. Smith 2003 Feedback control for the chemostat J. Math. Biol. 46 48 70 1015.92046 10.1007/s00285-002-0170-x 1957009 (Pubitemid 38355703)
    • (2003) Journal of Mathematical Biology , vol.46 , Issue.1 , pp. 48-70
    • De Leenheer, P.1    Smith, H.2
  • 4
    • 0031558482 scopus 로고    scopus 로고
    • Two distinct types of natural selection in turbidostat-like and chemostat-like ecosystems
    • DOI 10.1006/jtbi.1997.0458
    • J. Flegr 1997 Two distinct types of natural selection in turbidostat-like and chemostat-like ecosystems J. Theor. Biol. 188 121 126 10.1006/jtbi.1997. 0458 (Pubitemid 27421300)
    • (1997) Journal of Theoretical Biology , vol.188 , Issue.1 , pp. 121-126
    • Flegr, J.1
  • 6
    • 0018868854 scopus 로고
    • Single-nutrient microbial competition: Agreement between experimental and theoretical forecast outcomes
    • 10.1126/science.6767274
    • S.R. Hansen S.P. Hubbell 1980 Single-nutrient microbial competition: Agreement between experimental and theoretical forecast outcomes Science 207 1491 1493 10.1126/science.6767274
    • (1980) Science , vol.207 , pp. 1491-1493
    • Hansen, S.R.1    Hubbell, S.P.2
  • 7
    • 0000468175 scopus 로고
    • Limiting behavior for competing species
    • 0381.92014 10.1137/0134064 484548
    • S.B. Hsu 1978 Limiting behavior for competing species SIAM J. Appl. Math. 34 760 763 0381.92014 10.1137/0134064 484548
    • (1978) SIAM J. Appl. Math. , vol.34 , pp. 760-763
    • Hsu, S.B.1
  • 8
    • 0000875842 scopus 로고
    • A mathematical theory of single-nutrient competition in continuous cultures of microorganisms
    • 0354.92033 10.1137/0132030 434492
    • S.B. Hsu S. Hubbell P. Waltman 1977 A mathematical theory of single-nutrient competition in continuous cultures of microorganisms SIAM J. Appl. Math. 32 366 383 0354.92033 10.1137/0132030 434492
    • (1977) SIAM J. Appl. Math. , vol.32 , pp. 366-383
    • Hsu, S.B.1    Hubbell, S.2    Waltman, P.3
  • 9
    • 0001053926 scopus 로고
    • Coexistence in a variable environment
    • 10.1086/283527 597392
    • R. Levins 1979 Coexistence in a variable environment Am. Nat. 114 765 783 10.1086/283527 597392
    • (1979) Am. Nat. , vol.114 , pp. 765-783
    • Levins, R.1
  • 11
    • 37248999845 scopus 로고    scopus 로고
    • The dynamics of an age structured predator-prey model with disturbing pulse and time delays
    • DOI 10.1016/j.nonrwa.2006.12.001, PII S1468121806001647
    • X.Z. Meng J.J. Jiao L.S. Chen 2008 The dynamics of an age-structured predator-prey model with disturbing pulse and time delays Nonlinear Anal.: Real World Appl. 9 547 561 1142.34054 10.1016/j.nonrwa.2006.12.001 2382398 (Pubitemid 350267346)
    • (2008) Nonlinear Analysis: Real World Applications , vol.9 , Issue.2 , pp. 547-561
    • Meng, X.1    Jiao, J.2    Chen, L.3
  • 12
    • 0026818163 scopus 로고
    • Global dynamics of a mathematical model of competition in the chemostat: General response function and differential death rates
    • 0739.92025 10.1137/0152012 1148326
    • G.S.K. Wolkowicz Z. Lu 1992 Global dynamics of a mathematical model of competition in the chemostat: general response function and differential death rates SIAM J. Appl. Math. 52 222 233 0739.92025 10.1137/0152012 1148326
    • (1992) SIAM J. Appl. Math. , vol.52 , pp. 222-233
    • Wolkowicz, G.S.K.1    Lu, Z.2
  • 15
    • 26444534343 scopus 로고    scopus 로고
    • Existence of periodic solution of order one of planar impulsive autonomous system
    • DOI 10.1016/j.cam.2005.03.003, PII S0377042705001275
    • G.Z. Zeng L.S. Chen L.H. Sun 2006 Existence of periodic solution of order one of planer impulsive autonomous system J. Comput. Appl. Math. 186 466 481 1088.34040 10.1016/j.cam.2005.03.003 2176360 (Pubitemid 41433595)
    • (2006) Journal of Computational and Applied Mathematics , vol.186 , Issue.2 , pp. 466-481
    • Zeng, G.1    Chen, L.2    Sun, L.3
  • 16
    • 0041758422 scopus 로고    scopus 로고
    • Feedback control for chemostat models
    • DOI 10.1007/s00285-002-0170-x
    • P. De Leenheer H.L. Smith 2003 Feedback control for chemostat model J. Math. Biol. 46 48 70 1015.92046 10.1007/s00285-002-0170-x 1957009 (Pubitemid 38355703)
    • (2003) Journal of Mathematical Biology , vol.46 , Issue.1 , pp. 48-70
    • De Leenheer, P.1    Smith, H.2
  • 17
    • 70049090400 scopus 로고    scopus 로고
    • Competition in a turbidostat for an inhibitory nutrient
    • 1140.92324 10.1080/17513750802018345 2427528
    • B.T. Li 2008 Competition in a turbidostat for an inhibitory nutrient J. Biol. Dyn. 2 208 220 1140.92324 10.1080/17513750802018345 2427528
    • (2008) J. Biol. Dyn. , vol.2 , pp. 208-220
    • Li, B.T.1
  • 18
    • 70349553028 scopus 로고    scopus 로고
    • Existence of periodic solution of order one of state-dependent impulsive differential equations and its application in pest control
    • 1150.34442
    • G.Z. Zeng 2007 Existence of periodic solution of order one of state-dependent impulsive differential equations and its application in pest control J. Biomath. (in China) 22 4 652 660 1150.34442
    • (2007) J. Biomath. (In China) , vol.22 , Issue.4 , pp. 652-660
    • Zeng, G.Z.1
  • 19
    • 84950932738 scopus 로고
    • Orbital stability of periodic solutions autonomous systems with impulse effect
    • P.E. Simeonov D.D. Bainov 1988 Orbital stability of periodic solutions autonomous systems with impulse effect Int. J. Syst. Sci. 19 2562 2585
    • (1988) Int. J. Syst. Sci. , vol.19 , pp. 2562-2585
    • Simeonov, P.E.1    Bainov, D.D.2
  • 20
    • 33746005301 scopus 로고    scopus 로고
    • Complex dynamics of a Holling type II prey-predator system with state feedback control
    • DOI 10.1016/j.chaos.2005.09.077, PII S0960077905009458
    • G.R. Jiang Q.S. Lu L.N. Qian 2007 Complex dynamics of a Holling II prey-predator system with state feedback control Chaos Solitons Fractals 31 448 461 05264991 10.1016/j.chaos.2005.09.077 2259769 (Pubitemid 44067472)
    • (2007) Chaos, Solitons and Fractals , vol.31 , Issue.2 , pp. 448-461
    • Jiang, G.1    Lu, Q.2    Qian, L.3
  • 21
    • 84863116421 scopus 로고    scopus 로고
    • Permanence and global stability in an impulsive Lotka-Volterra N-Species competitive system with both discrete delays and continuous delays
    • 1155.92356 10.1142/S1793524508000151 2444295
    • X.Z. Meng L.S. Chen 2008 Permanence and global stability in an impulsive Lotka-Volterra N-Species competitive system with both discrete delays and continuous delays Int. J. Biomath. 1 179 196 1155.92356 10.1142/ S1793524508000151 2444295
    • (2008) Int. J. Biomath. , vol.1 , pp. 179-196
    • Meng, X.Z.1    Chen, L.S.2
  • 22
    • 84863116071 scopus 로고    scopus 로고
    • Global attractivity of a stage-structure variable coefficients of predator-prey system with time delay and impulsive perturbations on predators
    • 1155.92355 10.1142/S1793524508000163 2444296
    • J.J. Jiao L.S. Chen 2008 Global attractivity of a stage-structure variable coefficients of predator-prey system with time delay and impulsive perturbations on predators Int. J. Biomath. 1 197 208 1155.92355 10.1142/S1793524508000163 2444296
    • (2008) Int. J. Biomath. , vol.1 , pp. 197-208
    • Jiao, J.J.1    Chen, L.S.2
  • 23
    • 50249100273 scopus 로고    scopus 로고
    • Staged-structured Lotka-Volterra predator-prey models for pest management
    • 10.1016/j.amc.2008.04.032 2452283
    • R.Q. Shi L.S. Chen 2008 Staged-structured Lotka-Volterra predator-prey models for pest management Appl. Math. Comput. 10.1016/j.amc.2008.04.032 2452283
    • (2008) Appl. Math. Comput.
    • Shi, R.Q.1    Chen, L.S.2
  • 24
    • 58249128806 scopus 로고    scopus 로고
    • A predator-prey model with disease in the prey and two impulses for integrated pest management
    • doi: 10.1016/j.apm.2008.06.001
    • Shi, R.Q., Chen, L.S.: A predator-prey model with disease in the prey and two impulses for integrated pest management. Appl. Math. Model. doi: 10.1016/j.apm.2008.06.001
    • Appl. Math. Model
    • Shi, R.Q.1    Chen, L.S.2
  • 25
    • 2942670841 scopus 로고    scopus 로고
    • Modelling and analysis of integrated management strategy
    • 1114.92074 10.3934/dcdsb.2004.4.759 2073982
    • S.Y. Tang L.S. Chen 2004 Modelling and analysis of integrated management strategy Discrete Contin. Dyn. Syst., Ser. B 4 759 768 1114.92074 10.3934/dcdsb.2004.4.759 2073982
    • (2004) Discrete Contin. Dyn. Syst., Ser. B , vol.4 , pp. 759-768
    • Tang, S.Y.1    Chen, L.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.