메뉴 건너뛰기




Volumn 239, Issue 20-22, 2010, Pages 2011-2024

Stability and bifurcation analysis in hematopoietic stem cell dynamics with multiple delays

Author keywords

Global asymptotical stability; Hopf bifurcation; HSCs; Positive periodic solution

Indexed keywords

DIFFERENTIAL EQUATIONS; LYAPUNOV METHODS; PROBLEM SOLVING; STABILITY; STEM CELLS; TIME DELAY;

EID: 77956094912     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2010.07.013     Document Type: Article
Times cited : (24)

References (43)
  • 1
    • 0018138249 scopus 로고
    • Unified hypothesis of the origin of aplastic anaemia and periodic hematopoiesis
    • M.C. Mackey Unified hypothesis of the origin of aplastic anaemia and periodic hematopoiesis Blood 51 1978 941 956
    • (1978) Blood , vol.51 , pp. 941-956
    • MacKey, M.C.1
  • 3
    • 34648813587 scopus 로고    scopus 로고
    • Life and death in hematopoietic stem cells
    • H. Oguro, and A. Iwama Life and death in hematopoietic stem cells Curr. Opin. Immunol. 19 2007 503 509
    • (2007) Curr. Opin. Immunol. , vol.19 , pp. 503-509
    • Oguro, H.1    Iwama, A.2
  • 4
    • 52249107424 scopus 로고    scopus 로고
    • Asymptotic behavior of a discrete maturity structured system of hematopoietic stem cell dynamics with several delays
    • M. Adimy, F. Crauste, and A. El Abdllaoui Asymptotic behavior of a discrete maturity structured system of hematopoietic stem cell dynamics with several delays Math. Model. Nat. Phenom. 1 2 2006 1 20
    • (2006) Math. Model. Nat. Phenom. , vol.1 , Issue.2 , pp. 1-20
    • Adimy, M.1    Crauste, F.2    El Abdllaoui, A.3
  • 5
    • 52249093569 scopus 로고    scopus 로고
    • Discrete maturity-structured model of cell differentiation with applications to acute myelogenous leukemia
    • M. Adimy, F. Crauste, and A. El Abdllaoui Discrete maturity-structured model of cell differentiation with applications to acute myelogenous leukemia J. Biol. Syst. 1 3 2008 395 424
    • (2008) J. Biol. Syst. , vol.1 , Issue.3 , pp. 395-424
    • Adimy, M.1    Crauste, F.2    El Abdllaoui, A.3
  • 6
    • 24344475745 scopus 로고    scopus 로고
    • A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia
    • M. Adimy, F. Crauste, and S. Ruan A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia SIAM J. Appl. Math. 65 2005 1328 1352
    • (2005) SIAM J. Appl. Math. , vol.65 , pp. 1328-1352
    • Adimy, M.1    Crauste, F.2    Ruan, S.3
  • 7
    • 15844377066 scopus 로고    scopus 로고
    • Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics
    • M. Adimy, F. Crauste, and S. Ruan Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics Nonlinear Anal. RWA 6 2005 651 670
    • (2005) Nonlinear Anal. RWA , vol.6 , pp. 651-670
    • Adimy, M.1    Crauste, F.2    Ruan, S.3
  • 8
    • 33747479155 scopus 로고    scopus 로고
    • Periodic oscillations in leukopoiesis models with two delays
    • M. Adimy, F. Crauste, and S. Ruan Periodic oscillations in leukopoiesis models with two delays J. Theoret. Biol. 242 2006 288 299
    • (2006) J. Theoret. Biol. , vol.242 , pp. 288-299
    • Adimy, M.1    Crauste, F.2    Ruan, S.3
  • 10
    • 1842426546 scopus 로고    scopus 로고
    • Contribution to the study of periodic chronic myelogenous leukemia
    • L. Pujo-Menjouet, and M. Mackey Contribution to the study of periodic chronic myelogenous leukemia C. R. Biologies 327 2004 235 244
    • (2004) C. R. Biologies , vol.327 , pp. 235-244
    • Pujo-Menjouet, L.1    MacKey, M.2
  • 11
    • 43949124448 scopus 로고    scopus 로고
    • Bifurcation analysis in an approachable haematopoietic stem cells model
    • A. Wan, and J. Wei Bifurcation analysis in an approachable haematopoietic stem cells model J. Math. Anal. Appl. 345 2008 276 285
    • (2008) J. Math. Anal. Appl. , vol.345 , pp. 276-285
    • Wan, A.1    Wei, J.2
  • 12
    • 0038297622 scopus 로고    scopus 로고
    • Analysis of cell kinetics using a cell division marker: Mathematical analysis of experimental data
    • S. Bernard, L. Pujo-Menjouet, and M.C. Mackey Analysis of cell kinetics using a cell division marker: mathematical analysis of experimental data Biophys. J. 84 2003 3414 3424
    • (2003) Biophys. J. , vol.84 , pp. 3414-3424
    • Bernard, S.1    Pujo-Menjouet, L.2    MacKey, M.C.3
  • 13
    • 0347130009 scopus 로고    scopus 로고
    • Stability and bifurcation in a neural network model with two delays
    • J. Wei, and S. Ruan Stability and bifurcation in a neural network model with two delays Physica D 130 1999 255 272
    • (1999) Physica D , vol.130 , pp. 255-272
    • Wei, J.1    Ruan, S.2
  • 14
    • 1842465386 scopus 로고    scopus 로고
    • On the zeros of transcendental functions with applications to stability of delay differential equations with two delays
    • S. Ruan, and J. Wei On the zeros of transcendental functions with applications to stability of delay differential equations with two delays Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 10 2003 863 874
    • (2003) Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. , vol.10 , pp. 863-874
    • Ruan, S.1    Wei, J.2
  • 17
    • 33646864830 scopus 로고    scopus 로고
    • Symmetric functional differential equations and neural networks with memory
    • J. Wu Symmetric functional differential equations and neural networks with memory Trans. Amer. Math. Soc. 350 1998 4799 4838
    • (1998) Trans. Amer. Math. Soc. , vol.350 , pp. 4799-4838
    • Wu, J.1
  • 18
    • 35548967647 scopus 로고    scopus 로고
    • Bifurcation analysis in a scalar delay differential equation
    • J. Wei Bifurcation analysis in a scalar delay differential equation Nonlinearity 20 2007 2483 2498
    • (2007) Nonlinearity , vol.20 , pp. 2483-2498
    • Wei, J.1
  • 19
    • 34548462206 scopus 로고    scopus 로고
    • Hopf bifurcation analysis in a MackeyGlass system
    • J. Wei, and D. Fan Hopf bifurcation analysis in a MackeyGlass system Internat. J. Bifur. Chaos 17 6 2007 2149 2157
    • (2007) Internat. J. Bifur. Chaos , vol.17 , Issue.6 , pp. 2149-2157
    • Wei, J.1    Fan, D.2
  • 20
    • 12244312783 scopus 로고    scopus 로고
    • Hopf bifurcation analysis in a delayed Nicholson blowflies equation
    • J. Wei, and M.Y. Li Hopf bifurcation analysis in a delayed Nicholson blowflies equation Nonlinear Anal. 60 2005 1351 1367
    • (2005) Nonlinear Anal. , vol.60 , pp. 1351-1367
    • Wei, J.1    Li, M.Y.2
  • 21
    • 70149125199 scopus 로고    scopus 로고
    • Hopf bifurcation analysis in a model of oscillatory gene expression with delay
    • J. Wei, and C. Yu Hopf bifurcation analysis in a model of oscillatory gene expression with delay Proc. Roy. Soc. Edinburgh Sect. A. 139 2009 879 895
    • (2009) Proc. Roy. Soc. Edinburgh Sect. A. , vol.139 , pp. 879-895
    • Wei, J.1    Yu, C.2
  • 23
    • 77952672921 scopus 로고
    • Convergence results and a PoincarBendixson trichotomy for asymptotically autonomous differential equations
    • H. Thieme Convergence results and a PoincarBendixson trichotomy for asymptotically autonomous differential equations J. Math. Biol. 30 1992 755 763
    • (1992) J. Math. Biol. , vol.30 , pp. 755-763
    • Thieme, H.1
  • 24
    • 0036568042 scopus 로고    scopus 로고
    • Existence and stability of periodic solutions for Hopfield neural network equations with periodic input
    • Q. Dong, K. Matsui, and X. Huang Existence and stability of periodic solutions for Hopfield neural network equations with periodic input Nonlinear Anal. 49 2002 471 479
    • (2002) Nonlinear Anal. , vol.49 , pp. 471-479
    • Dong, Q.1    Matsui, K.2    Huang, X.3
  • 25
    • 0000695051 scopus 로고
    • Coincidence degree and periodic solutions of neutral equations
    • J. Hale, and J. Mawhin Coincidence degree and periodic solutions of neutral equations J. Differential Equations 15 1974 295 307
    • (1974) J. Differential Equations , vol.15 , pp. 295-307
    • Hale, J.1    Mawhin, J.2
  • 26
    • 0016037121 scopus 로고
    • Periodic solutions of some vector retarded functional differential equation
    • J. Mawhin Periodic solutions of some vector retarded functional differential equation J. Math. Anal. Appl. 45 1974 588 603
    • (1974) J. Math. Anal. Appl. , vol.45 , pp. 588-603
    • Mawhin, J.1
  • 27
    • 0035285146 scopus 로고    scopus 로고
    • Periodic solution of periodic delay LotkaVolterra equations and systems
    • Y. Li, and Y. Kuang Periodic solution of periodic delay LotkaVolterra equations and systems J. Math. Anal. Appl. 255 2001 260 280
    • (2001) J. Math. Anal. Appl. , vol.255 , pp. 260-280
    • Li, Y.1    Kuang, Y.2
  • 28
    • 0036373967 scopus 로고    scopus 로고
    • Geometric stability switch criteria in delay differential systems with delay dependant parameters
    • E. Beretta, and Y. Kuang Geometric stability switch criteria in delay differential systems with delay dependant parameters SIAM. J. Math. Anal. 33 2002 1144 1165
    • (2002) SIAM. J. Math. Anal. , vol.33 , pp. 1144-1165
    • Beretta, E.1    Kuang, Y.2
  • 29
    • 34248370155 scopus 로고    scopus 로고
    • Bifurcation analysis in a time-delay model for preypredator growth with stage-structure
    • Y. Qu, and J. Wei Bifurcation analysis in a time-delay model for preypredator growth with stage-structure Nonlinear Dynam. 49 2007 285 294
    • (2007) Nonlinear Dynam. , vol.49 , pp. 285-294
    • Qu, Y.1    Wei, J.2
  • 30
    • 77955473046 scopus 로고    scopus 로고
    • Bifurcation analysis in a predatorprey system with stage-structure and harvesting
    • Y. Qu, and J. Wei Bifurcation analysis in a predatorprey system with stage-structure and harvesting J. Franklin Inst. 347 2010 1097 1113
    • (2010) J. Franklin Inst. , vol.347 , pp. 1097-1113
    • Qu, Y.1    Wei, J.2
  • 31
    • 0042698639 scopus 로고
    • Cambridge University Press Cambridge
    • P. John The Cell Cycle 1981 Cambridge University Press Cambridge
    • (1981) The Cell Cycle
    • John, P.1
  • 34
    • 33750733928 scopus 로고    scopus 로고
    • Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases
    • M. Adimy, F. Crauste, and S. Ruan Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases Bull. Math. Biol. 68 2006 2321 2351
    • (2006) Bull. Math. Biol. , vol.68 , pp. 2321-2351
    • Adimy, M.1    Crauste, F.2    Ruan, S.3
  • 35
    • 84960560867 scopus 로고
    • Roots of the transcendental equation associated with a certain differential difference equation
    • N. Hayes Roots of the transcendental equation associated with a certain differential difference equation J. Lond. Math. Soc. 25 1950 226 232
    • (1950) J. Lond. Math. Soc. , vol.25 , pp. 226-232
    • Hayes, N.1
  • 36
    • 0000840165 scopus 로고
    • Normal forms for retarded functional differential equations and applications to BagdanovTakens singularity
    • T. Faria, and L. Magalhes Normal forms for retarded functional differential equations and applications to BagdanovTakens singularity J. Differential Equations 122 1995 201 224
    • (1995) J. Differential Equations , vol.122 , pp. 201-224
    • Faria, T.1    Magalhes, L.2
  • 37
    • 0039483059 scopus 로고    scopus 로고
    • Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL
    • K. Engelborghs, T. Luzyanina, and D. Roose Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL ACM Trans. Math. Software 28 2002 1 21
    • (2002) ACM Trans. Math. Software , vol.28 , pp. 1-21
    • Engelborghs, K.1    Luzyanina, T.2    Roose, D.3
  • 38
  • 39
    • 0038205228 scopus 로고
    • Asymptotically autonomous differential systems S. Lefschetz, Contributions to the Theory of Nonlinear Oscillations III
    • U. Markus Asymptotically autonomous differential systems S. Lefschetz, Contributions to the Theory of Nonlinear Oscillations III Ann. Math. Stud. vol. 36 1956 Princeton University Press Princeton 17 29
    • (1956) Ann. Math. Stud. , vol.36 , pp. 17-29
    • Markus, U.1
  • 40
    • 0032532631 scopus 로고    scopus 로고
    • Cyclical neutropenia and other periodic hematological diseases: A review of mechanisms and mathematical models
    • C. Haurie, D. Dale, and M.C. Mackey Cyclical neutropenia and other periodic hematological diseases: a review of mechanisms and mathematical models Blood 92 1998 2629 2640
    • (1998) Blood , vol.92 , pp. 2629-2640
    • Haurie, C.1    Dale, D.2    MacKey, M.C.3
  • 42
    • 59649113905 scopus 로고    scopus 로고
    • Dynamic hematological disease: A review
    • C. Foley, and M.C. Mackey Dynamic hematological disease: a review J. Math. Biol. 58 2009 285 322
    • (2009) J. Math. Biol. , vol.58 , pp. 285-322
    • Foley, C.1    MacKey, M.C.2
  • 43
    • 0032956844 scopus 로고    scopus 로고
    • Periodic chronic myelogenous leukemia: Spectral analysis of blood cell counts and etiological implications
    • P. Fortin, and M.C. Mackey Periodic chronic myelogenous leukemia: spectral analysis of blood cell counts and etiological implications British J. Haematol. 104 1999 336 345
    • (1999) British J. Haematol. , vol.104 , pp. 336-345
    • Fortin, P.1    MacKey, M.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.