메뉴 건너뛰기




Volumn 41, Issue 5, 2009, Pages 2491-2494

Hopf bifurcation of a free boundary problem modeling tumor growth with two time delays

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; CELL DEATH; TIME DELAY; TUMORS;

EID: 67649365995     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2008.09.029     Document Type: Article
Times cited : (16)

References (19)
  • 1
    • 0007894647 scopus 로고    scopus 로고
    • The nonnegativity of solutions of delay differential equations
    • Bodnar M. The nonnegativity of solutions of delay differential equations. Appl. Math. Lett. 13 (2000)
    • (2000) Appl. Math. Lett. , vol.13
    • Bodnar, M.1
  • 2
    • 0028790729 scopus 로고
    • Growth of nonnecrotic tumors in the presence and absence of inhibitors
    • Byrne H., and Chaplain M. Growth of nonnecrotic tumors in the presence and absence of inhibitors. Math. Biosci. 130 (1995) 151-181
    • (1995) Math. Biosci. , vol.130 , pp. 151-181
    • Byrne, H.1    Chaplain, M.2
  • 3
    • 0030586186 scopus 로고    scopus 로고
    • Growth of necrotic tumors in the presence and absence of inhibitors
    • Byrne H., and Chaplain M. Growth of necrotic tumors in the presence and absence of inhibitors. Math. Biosci. 135 (1996) 187-216
    • (1996) Math. Biosci. , vol.135 , pp. 187-216
    • Byrne, H.1    Chaplain, M.2
  • 4
    • 0034040582 scopus 로고    scopus 로고
    • Analysis of a mathematical model of the effect of inhibitors on the growth of tumors
    • Cui S., and Friedman A. Analysis of a mathematical model of the effect of inhibitors on the growth of tumors. Math. Biosci. 164 (2000) 103-137
    • (2000) Math. Biosci. , vol.164 , pp. 103-137
    • Cui, S.1    Friedman, A.2
  • 5
    • 0035869870 scopus 로고    scopus 로고
    • Analysis of a mathematical model of the growth of necrotic tumors
    • Cui S., and Friedman A. Analysis of a mathematical model of the growth of necrotic tumors. J. Math. Anal. Appl. 255 (2001) 636-677
    • (2001) J. Math. Anal. Appl. , vol.255 , pp. 636-677
    • Cui, S.1    Friedman, A.2
  • 6
    • 34547133457 scopus 로고    scopus 로고
    • Analysis of mathematical models for the growth of tumors with time delays in cell proliferation
    • Cui S., and Xu S. Analysis of mathematical models for the growth of tumors with time delays in cell proliferation. J. Math. Anal. Appl. 336 (2007) 523-541
    • (2007) J. Math. Anal. Appl. , vol.336 , pp. 523-541
    • Cui, S.1    Xu, S.2
  • 7
    • 0020453046 scopus 로고
    • Migration and internalization of cells and polystyrene microspheres in tumor cell spheroids
    • Dorie M., Kallman R., Rapacchietta D., et al. Migration and internalization of cells and polystyrene microspheres in tumor cell spheroids. Exp. Cell Res. 141 (1982) 201-209
    • (1982) Exp. Cell Res. , vol.141 , pp. 201-209
    • Dorie, M.1    Kallman, R.2    Rapacchietta, D.3
  • 8
    • 0033094895 scopus 로고    scopus 로고
    • Analysis of a mathematical model for the growth of tumors
    • Friedman A., and Reitich F. Analysis of a mathematical model for the growth of tumors. J. Math. Biol. 38 (1999) 262-284
    • (1999) J. Math. Biol. , vol.38 , pp. 262-284
    • Friedman, A.1    Reitich, F.2
  • 9
    • 0000128125 scopus 로고
    • Models for the growth of solid tumor by diffusion
    • Greenspan H. Models for the growth of solid tumor by diffusion. Stud. Appl. Math. 51 (1972) 317-340
    • (1972) Stud. Appl. Math. , vol.51 , pp. 317-340
    • Greenspan, H.1
  • 10
    • 0017198676 scopus 로고
    • On the growth and stability of cell cultures and solid tumors
    • Greenspan H. On the growth and stability of cell cultures and solid tumors. J. Theor. Biol. 56 (1976) 229-242
    • (1976) J. Theor. Biol. , vol.56 , pp. 229-242
    • Greenspan, H.1
  • 12
    • 0005828897 scopus 로고    scopus 로고
    • Stability and bifurcation in delay-differential equations with two delays
    • Li X., Ruan S., Wei J., et al. 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
  • 13
    • 4644254239 scopus 로고    scopus 로고
    • Hopf and resonant codimension two bifurcation in van der Pol equation with two time delays
    • Liao X.F. Hopf and resonant codimension two bifurcation in van der Pol equation with two time delays. Chaos, Solitons & Fractals 23 (2005) 857-871
    • (2005) Chaos, Solitons & Fractals , vol.23 , pp. 857-871
    • Liao, X.F.1
  • 14
    • 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
  • 15
    • 38849171712 scopus 로고    scopus 로고
    • Hopf bifurcation in a solid asascular tumor growth model with two discrete delays
    • 10.1016/j.mcm.2007.02.030
    • Piotrowska M.J. Hopf bifurcation in a solid asascular tumor growth model with two discrete delays. Math. Comput. Mod. (2007) 10.1016/j.mcm.2007.02.030
    • (2007) Math. Comput. Mod.
    • Piotrowska, M.J.1
  • 16
    • 0032838793 scopus 로고    scopus 로고
    • Modelling the internalisation of labelled cells in tumor spheroids
    • Thompson K., and Byrne H. Modelling the internalisation of labelled cells in tumor spheroids. Bull. Math. Biol. 61 (1999) 601-623
    • (1999) Bull. Math. Biol. , vol.61 , pp. 601-623
    • Thompson, K.1    Byrne, H.2
  • 17
    • 0347130009 scopus 로고    scopus 로고
    • Stability and bifurcation in a neural network model with two delays
    • Wei J., and Ruan S. 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
  • 18
    • 1642312070 scopus 로고    scopus 로고
    • Direction and stability of bifurcating periodic solutions of a chemostat model with two distributed delays
    • Yuan S., Song Y., and Han M. Direction and stability of bifurcating periodic solutions of a chemostat model with two distributed delays. Chaos, Solitons & Fractals 21 (2004) 1109-1123
    • (2004) Chaos, Solitons & Fractals , vol.21 , pp. 1109-1123
    • Yuan, S.1    Song, Y.2    Han, M.3
  • 19
    • 0347355137 scopus 로고    scopus 로고
    • Bifurcation analysis of a chemostat model with two distributed delays
    • Yuan S., and Han M. Bifurcation analysis of a chemostat model with two distributed delays. Chaos, Solitons & Fractals 20 (2004) 995-1004
    • (2004) Chaos, Solitons & Fractals , vol.20 , pp. 995-1004
    • Yuan, S.1    Han, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.