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Volumn 47, Issue 5-6, 2008, Pages 597-603

Hopf bifurcation in a solid avascular tumour growth model with two discrete delays

Author keywords

Delays; Hopf bifurcation; Solid avascular tumour; Stability

Indexed keywords

CELL DEATH; CELL GROWTH; HOPF BIFURCATION; MATHEMATICAL MODELS; PARAMETER ESTIMATION; TIME DELAY;

EID: 38849171712     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2007.02.030     Document Type: Article
Times cited : (50)

References (30)
  • 1
    • 4544277958 scopus 로고    scopus 로고
    • Preziosi L. (Ed), Chapman & Hall/CRC, London
    • In: Preziosi L. (Ed). Cancer Modeling and Simulation (2003), Chapman & Hall/CRC, London
    • (2003) Cancer Modeling and Simulation
  • 2
    • 0028120597 scopus 로고
    • Dynamics of tumour interaction with the host immune system
    • Bellomo N., and Forni G. Dynamics of tumour interaction with the host immune system. Math. Comput. Modelling 20 (1994) 107-122
    • (1994) Math. Comput. Modelling , vol.20 , pp. 107-122
    • Bellomo, N.1    Forni, G.2
  • 4
    • 27644503155 scopus 로고    scopus 로고
    • Micro and meso scales of description corresponding to a model of tissue invasion by solid tumours
    • Lachowicz M. Micro and meso scales of description corresponding to a model of tissue invasion by solid tumours. Math. Models Methods Appl. Sci. 15 (2005) 1639-1666
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , pp. 1639-1666
    • Lachowicz, M.1
  • 5
    • 27644463491 scopus 로고    scopus 로고
    • Mathematical modeling of cancer cell invasion of tissue: The role of the urokinase plasminogen activation system
    • Chaplain M.A.J., and Lolas G. Mathematical modeling of cancer cell invasion of tissue: The role of the urokinase plasminogen activation system. Math. Models Methods Appl. Sci. 15 (2005) 1685-1734
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , pp. 1685-1734
    • Chaplain, M.A.J.1    Lolas, G.2
  • 6
    • 27644540984 scopus 로고    scopus 로고
    • A mathematical model for tumor cords incorporating the flow of interstitial fluid
    • Bertuzzi A., Fasano A., and Gandolfi A. A mathematical model for tumor cords incorporating the flow of interstitial fluid. Math. Models Methods Appl. Sci. 15 (2005) 1735-1777
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , pp. 1735-1777
    • Bertuzzi, A.1    Fasano, A.2    Gandolfi, A.3
  • 8
    • 0035819775 scopus 로고    scopus 로고
    • Resonance in periodic chemotherapy: A case study of acute myelogenous leukemia
    • Andersen L.K., and Mackey M.C. Resonance in periodic chemotherapy: A case study of acute myelogenous leukemia. J. Theoret. Biol. 209 (2001) 113-130
    • (2001) J. Theoret. Biol. , vol.209 , pp. 113-130
    • Andersen, L.K.1    Mackey, M.C.2
  • 9
    • 1642344491 scopus 로고    scopus 로고
    • A mathematical model for chronic myelogenous leukemia (cml) and t cell interaction
    • Moore H., and Lib N.K. A mathematical model for chronic myelogenous leukemia (cml) and t cell interaction. J. Theoret. Biol. 227 (2004) 513-523
    • (2004) J. Theoret. Biol. , vol.227 , pp. 513-523
    • Moore, H.1    Lib, N.K.2
  • 10
    • 1842426546 scopus 로고    scopus 로고
    • Contribution to the study of periodic chronic myelogenous leukemia
    • Pujo-Menjouet L., and Mackey M.C. Contribution to the study of periodic chronic myelogenous leukemia. C. R. Acad. Sci. Paris Biol. 327 (2004) 235-244
    • (2004) C. R. Acad. Sci. Paris Biol. , vol.327 , pp. 235-244
    • Pujo-Menjouet, L.1    Mackey, M.C.2
  • 11
    • 0035348998 scopus 로고    scopus 로고
    • Spatio-temporal pattern formation on spherical surfaces: Numerical simulation and application to solid tumour growth
    • Chaplain M.A.J., Ganesh M., and Graham I.G. Spatio-temporal pattern formation on spherical surfaces: Numerical simulation and application to solid tumour growth. J. Math. Biol. 42 (2001) 387-423
    • (2001) J. Math. Biol. , vol.42 , pp. 387-423
    • Chaplain, M.A.J.1    Ganesh, M.2    Graham, I.G.3
  • 12
    • 0002964937 scopus 로고    scopus 로고
    • Avascular growth, angiogenesis and vascular growth in solid tumours: The mathematical modelling of the stages of tumour development
    • Chaplain M.A.J. Avascular growth, angiogenesis and vascular growth in solid tumours: The mathematical modelling of the stages of tumour development. Math. Comput. Modelling 23 (1996) 47-87
    • (1996) Math. Comput. Modelling , vol.23 , pp. 47-87
    • Chaplain, M.A.J.1
  • 13
    • 0030431867 scopus 로고    scopus 로고
    • On the role of cell-cell adhesion in models for solid tumour growth
    • Byrne H.M., and Chaplain M.A.J. On the role of cell-cell adhesion in models for solid tumour growth. Math. Comput. Modelling 24 (1996) 1-17
    • (1996) Math. Comput. Modelling , vol.24 , pp. 1-17
    • Byrne, H.M.1    Chaplain, M.A.J.2
  • 14
    • 34547102059 scopus 로고    scopus 로고
    • Time delay in necrotic core formation
    • Bodnar M., and Foryś U. Time delay in necrotic core formation. Math. Biosci. Eng. 2 (2005) 461-472
    • (2005) Math. Biosci. Eng. , vol.2 , pp. 461-472
    • Bodnar, M.1    Foryś, U.2
  • 15
    • 28844493432 scopus 로고    scopus 로고
    • Solid tumour growth. Analysis of necrotic core formation
    • Foryś U., and Mokwa-Borkowska A. Solid tumour growth. Analysis of necrotic core formation. Math. Comput. Modelling 42 (2005) 593-600
    • (2005) Math. Comput. Modelling , vol.42 , pp. 593-600
    • Foryś, U.1    Mokwa-Borkowska, A.2
  • 16
    • 14044250250 scopus 로고    scopus 로고
    • Modelling avascular tumour growth
    • Preziosi L. (Ed), Chapman & Hall/CRC, London
    • Byrne H.M. Modelling avascular tumour growth. In: Preziosi L. (Ed). Cancer Modeling and Simulation (2003), Chapman & Hall/CRC, London
    • (2003) Cancer Modeling and Simulation
    • Byrne, H.M.1
  • 18
    • 1942510670 scopus 로고    scopus 로고
    • Time delays in proliferation process for solid avascular tumour
    • Bodnar M., and Foryś U. Time delays in proliferation process for solid avascular tumour. Math. Comput. Modelling 37 (2003) 1201-1209
    • (2003) Math. Comput. Modelling , vol.37 , pp. 1201-1209
    • Bodnar, M.1    Foryś, U.2
  • 19
    • 0038575163 scopus 로고    scopus 로고
    • Time delays in regulatory apoptosis for solid avascular tumour
    • Bodnar M., and Foryś U. Time delays in regulatory apoptosis for solid avascular tumour. Math. Comput. Modelling 37 (2003) 1211-1220
    • (2003) Math. Comput. Modelling , vol.37 , pp. 1211-1220
    • Bodnar, M.1    Foryś, U.2
  • 20
    • 0030822132 scopus 로고    scopus 로고
    • The effect of time delays on the dynamics of avascular tumour growth
    • Byrne H.M. The effect of time delays on the dynamics of avascular tumour growth. Math. Biosci. 144 (1997) 83-117
    • (1997) Math. Biosci. , vol.144 , pp. 83-117
    • Byrne, H.M.1
  • 21
    • 38849158074 scopus 로고    scopus 로고
    • M.J. Piotrowska, U. Foryś, Time delays in avascular tumour growth, in: Proceedings of the Tenth National Conference on Application of Mathematics in Biology and Medicine, Świȩty Krzyż, 22-25 September 2004, 2004, pp. 43-48
    • M.J. Piotrowska, U. Foryś, Time delays in avascular tumour growth, in: Proceedings of the Tenth National Conference on Application of Mathematics in Biology and Medicine, Świȩty Krzyż, 22-25 September 2004, 2004, pp. 43-48
  • 22
    • 33749445055 scopus 로고    scopus 로고
    • Time delays in proliferation and apoptosis for solid avascular tumour
    • Foryś U., and Kolev M. Time delays in proliferation and apoptosis for solid avascular tumour. Math Model. Popul. Dynam. 63 (2004) 187-196
    • (2004) Math Model. Popul. Dynam. , vol.63 , pp. 187-196
    • Foryś, U.1    Kolev, M.2
  • 24
    • 0007894647 scopus 로고    scopus 로고
    • The nonnegativity of solutions of delay differential equation
    • Bodnar M. The nonnegativity of solutions of delay differential equation. Appl. Math. Lett. 13 (2000) 91-95
    • (2000) Appl. Math. Lett. , vol.13 , pp. 91-95
    • Bodnar, M.1
  • 26
    • 7044226613 scopus 로고    scopus 로고
    • Biological delay systems and Mikhailov criterion of stability
    • Foryś U. Biological delay systems and Mikhailov criterion of stability. J. Biol. Syst. 12 (2004) 45-60
    • (2004) J. Biol. Syst. , vol.12 , pp. 45-60
    • Foryś, U.1
  • 28
    • 0005828897 scopus 로고    scopus 로고
    • Stability and bifurcation in delay-differential equations with two delays
    • Li X., Ruan S., and Wei J. Stability and bifurcation in delay-differential equations with two delays. J. Math. Anal. Appl. 236 (1999) 254-280
    • (1999) J. Math. Anal. Appl. , vol.236 , pp. 254-280
    • Li, X.1    Ruan, S.2    Wei, J.3
  • 29
    • 33846305414 scopus 로고    scopus 로고
    • A remark on the ODE with two discrete delays
    • Piotrowska M.J. A remark on the ODE with two discrete delays. J. Math. Anal. Appl. 329 (2007) 664-676
    • (2007) J. Math. Anal. Appl. , vol.329 , pp. 664-676
    • Piotrowska, M.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.