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Volumn 357, Issue 10, 2005, Pages 3953-3969

Turing patterns in the Lengyel-Epstein system for the CIMA reaction

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EID: 26444473202     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-05-04010-9     Document Type: Article
Times cited : (153)

References (17)
  • 1
    • 0346072299 scopus 로고    scopus 로고
    • Pattern formation in three-dimensional reaction-diffusion systems
    • [CK]. MR1701288 (2000e:35098)
    • [CK] T. K. CALLAHAN AND E. KNOBLOCH, Pattern formation in three-dimensional reaction-diffusion systems, Phys. D 132, 339-362 (1999). MR1701288 (2000e:35098)
    • (1999) Phys. D , vol.132 , pp. 339-362
    • Callahan, T.K.1    Knobloch, E.2
  • 2
    • 0017537565 scopus 로고
    • Stability properties of solutions to systems of reaction-diffusion equations
    • [CH]. MR447760 (56 #6070)
    • [CH] R. G. CASTEN AND C. J. HOLLAND, Stability properties of solutions to systems of reaction-diffusion equations, SIAM J. Appl. Math. 33, 353-364 (1977). MR447760 (56 #6070)
    • (1977) SIAM J. Appl. Math. , vol.33 , pp. 353-364
    • Casten, R.G.1    Holland, C.J.2
  • 3
    • 5544250703 scopus 로고
    • Experimental evidence of a sustained Turing-type equilibrium chemical pattern
    • [CDBD]
    • [CDBD] V. CASTETS, E. DULOS, J. BOISSONADE AND P. DE KEPPER, Experimental evidence of a sustained Turing-type equilibrium chemical pattern, Phys. Rev. Lett. 64, 2953-2956 (1990).
    • (1990) Phys. Rev. Lett. , vol.64 , pp. 2953-2956
    • Castets, V.1    Dulos, E.2    Boissonade, J.3    De Kepper, P.4
  • 4
    • 44949270147 scopus 로고
    • Turing-type chemical patterns in the chlorite-iodide-malonic acid reaction
    • [DCDB]
    • [DCDB] P. DE KEPPER, V. CASTETS, E. DULOS AND J. BOISSONADE, Turing-type chemical patterns in the chlorite-iodide-malonic acid reaction, Physica D 49, 161-169 (1991).
    • (1991) Physica D , vol.49 , pp. 161-169
    • De Kepper, P.1    Castets, V.2    Dulos, E.3    Boissonade, J.4
  • 5
    • 84881625377 scopus 로고
    • Partial differential equations of parabolic type
    • [F]. MR0181836 (31 #6062)
    • [F] A. FRIEDMAN, Partial Differential Equations of Parabolic Type. Prentice-Hall: Englewood Cliffs, NJ, 1964. MR0181836 (31 #6062)
    • (1964) Prentice-hall: Englewood Cliffs, NJ
    • Friedman, A.1
  • 6
    • 0015454185 scopus 로고
    • A theory of biological pattern formation
    • [GM]
    • [GM] A. GIERER AND H. MEINHARDT, A theory of biological pattern formation, Kybernetik 12, 30-39 (1972).
    • (1972) Kybernetik , vol.12 , pp. 30-39
    • Gierer, A.1    Meinhardt, H.2
  • 7
    • 26444528184 scopus 로고    scopus 로고
    • Global bifurcation and structure of Turing patterns in 1-D Lengyel-Epstein model
    • [JNT]. MR2105777
    • [JNT] J. JANG, W.-M. NI AND M. TANG, Global bifurcation and structure of Turing patterns in 1-D Lengyel-Epstein model, J. Dynam. Diff. Eqs. 16 297-320 (2004). MR2105777
    • (2004) J. Dynam. Diff. Eqs. , vol.16 , pp. 297-320
    • Jang, J.1    Ni, W.-M.2    Tang, M.3
  • 8
    • 0001013465 scopus 로고    scopus 로고
    • Computer simulations of Turing structures in the Chlorite-Iodide-Malonic Acid system
    • [JMBD]
    • [JMBD] O. JENSEN, E. MOSEKILDE, P. BORCKMANS AND G. DEWEL, Computer simulations of Turing structures in the Chlorite-Iodide-Malonic Acid system, Physica Scripta 53, 243-251 (1996).
    • (1996) Physica Scripta , vol.53 , pp. 243-251
    • Jensen, O.1    Mosekilde, E.2    Borckmans, P.3    Dewel, G.4
  • 9
    • 0346057261 scopus 로고    scopus 로고
    • Simple and superlattice Turing patterns in reaction-diffusion systems: Bifurcation, bistability, and parameter collapse
    • [JS]. MR1732305 (2001a:37125)
    • [JS] S. L. JUDD AND M. SILBER, Simple and superlattice Turing patterns in reaction-diffusion systems: bifurcation, bistability, and parameter collapse, Phys. D 136, 45-65 (2000). MR1732305 (2001a:37125)
    • (2000) Phys. D , vol.136 , pp. 45-65
    • Judd, S.L.1    Silber, M.2
  • 10
    • 12044256206 scopus 로고
    • Modeling of Turing structures in the chlorite-iodide-malonic acid-starch reaction system
    • [LE1]
    • [LE1] I. LENGYEL AND I. R. EPSTEIN, Modeling of Turing structures in the chlorite-iodide-malonic acid-starch reaction system, Science 251, 650-652 (1991).
    • (1991) Science , vol.251 , pp. 650-652
    • Lengyel, I.1    Epstein, I.R.2
  • 11
    • 0026575824 scopus 로고
    • A chemical approach to designing Turing patterns in reaction-diffusion systems
    • [LE2]
    • [LE2] I. LENGYEL AND I. R. EPSTEIN, A chemical approach to designing Turing patterns in reaction-diffusion systems, Proc. Natl. Acad. Sci. USA 89, 3977-3979 (1992).
    • (1992) Proc. Natl. Acad. Sci. USA , vol.89 , pp. 3977-3979
    • Lengyel, I.1    Epstein, I.R.2
  • 12
    • 0030579038 scopus 로고    scopus 로고
    • Diffusion, self-diffusion and cross-diffusion
    • [LN]. MR1415047 (971:35086)
    • [LN] Y. LOU AND W.-M. NI, Diffusion, self-diffusion and cross-diffusion, J. Differential Equations 131, 79-131 (1996). MR1415047 (971:35086)
    • (1996) J. Differential Equations , vol.131 , pp. 79-131
    • Lou, Y.1    Ni, W.-M.2
  • 13
    • 0003002827 scopus 로고    scopus 로고
    • Diffusion, cross-diffusion, and their spike-layer steady states
    • [N]. MR1490535 (99a:35132)
    • [N] W.-M. NI, Diffusion, cross-diffusion, and their spike-layer steady states, Notices Amer. Math. Soc. 45, 9-18 (1998). MR1490535 (99a:35132)
    • (1998) Notices Amer. Math. Soc. , vol.45 , pp. 9-18
    • Ni, W.-M.1
  • 16
    • 0343807197 scopus 로고    scopus 로고
    • Chemical Turing pattern formation analyses: Comparison of theory with experiment
    • [WS]. MR1780797 (2001g:76062)
    • [WS] D. J. WOLLKIND AND L. E. STEPHENSON, Chemical Turing pattern formation analyses: comparison of theory with experiment, SIAM J. Appl. Math. 61, 387-431 (2000). MR1780797 (2001g:76062)
    • (2000) SIAM J. Appl. Math. , vol.61 , pp. 387-431
    • Wollkind, D.J.1    Stephenson, L.E.2
  • 17
    • 0000530223 scopus 로고
    • Invariant sets for weakly coupled parabolic and elliptic systems
    • [W]. MR0397126 (53 #986)
    • [W] H. F. WEINBERGER, Invariant sets for weakly coupled parabolic and elliptic systems, Rend. Mat. 8, 295-310 (1975). MR0397126 (53 #986)
    • (1975) Rend. Mat. , vol.8 , pp. 295-310
    • Weinberger, H.F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.