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Volumn 180, Issue 3-4, 2003, Pages 185-209

Pattern formation in a simple chemical system with general orders of autocatalysis and decay. I. Stability analysis

Author keywords

Pattern formation; Stability analysis; Travelling wave

Indexed keywords

MATHEMATICAL MODELS; PARAMETER ESTIMATION; REACTION KINETICS; STABILITY;

EID: 0038823713     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(03)00065-4     Document Type: Article
Times cited : (9)

References (33)
  • 2
    • 0013238621 scopus 로고    scopus 로고
    • On stability and Hopf bifurcations for chemotaxis systems
    • Dancer E.N., On stability and Hopf bifurcations for chemotaxis systems. Meth. Appl. Anal. 8(2):2001;245-256.
    • (2001) Meth. Appl. Anal. , vol.8 , Issue.2 , pp. 245-256
    • Dancer, E.N.1
  • 3
    • 0034912344 scopus 로고    scopus 로고
    • Slowly modulated two-pulse solutions in the Gray-Scott model. I. Asymptotic construction and stability
    • Doelman A., Eckhaus W., Kaper T.J., Slowly modulated two-pulse solutions in the Gray-Scott model. I. Asymptotic construction and stability. SIAM J. Appl. Math. 61(3):2000;1080-1102.
    • (2000) SIAM J. Appl. Math. , vol.61 , Issue.3 , pp. 1080-1102
    • Doelman, A.1    Eckhaus, W.2    Kaper, T.J.3
  • 4
    • 0035704463 scopus 로고    scopus 로고
    • Slowly modulated two-pulse solutions in the Gray-Scott model. II. Geometric theory, bifurcations, and splitting dynamics
    • Doelman A., Eckhaus W., Kaper T.J., Slowly modulated two-pulse solutions in the Gray-Scott model. II. Geometric theory, bifurcations, and splitting dynamics. SIAM J. Appl. Math. 61(6):2001;2036-2062.
    • (2001) SIAM J. Appl. Math. , vol.61 , Issue.6 , pp. 2036-2062
    • Doelman, A.1    Eckhaus, W.2    Kaper, T.J.3
  • 5
    • 0005468518 scopus 로고    scopus 로고
    • Stability analysis of singular patterns in the 1D Gray-Scott model: A matched asymptotics approach
    • Doelman A., Gardner R.A., Kaper T.J., Stability analysis of singular patterns in the 1D Gray-Scott model: a matched asymptotics approach. Physica D. 122:1998;1-36.
    • (1998) Physica D , vol.122 , pp. 1-36
    • Doelman, A.1    Gardner, R.A.2    Kaper, T.J.3
  • 6
    • 0000706319 scopus 로고    scopus 로고
    • Pattern formation in the one-dimensional Gray-Scott model
    • Doelman A., Kaper T.J., Zegeling P.A., Pattern formation in the one-dimensional Gray-Scott model. Nonlinearity. 10:1997;523-563.
    • (1997) Nonlinearity , vol.10 , pp. 523-563
    • Doelman, A.1    Kaper, T.J.2    Zegeling, P.A.3
  • 9
  • 10
    • 0036852057 scopus 로고    scopus 로고
    • On an initial-boundary-value problem for a coupled, singular reaction-diffusion system arising from a model of fractional order chemical autocatalysis and decay
    • P.M. McCabe, J.A. Leach, D.J. Needham, On an initial-boundary-value problem for a coupled, singular reaction-diffusion system arising from a model of fractional order chemical autocatalysis and decay, Quart. J. Mech. Appl. Math. 55 (2002) 511-560.
    • (2002) Quart. J. Mech. Appl. Math. , vol.55 , pp. 511-560
    • McCabe, P.M.1    Leach, J.A.2    Needham, D.J.3
  • 11
    • 0344211077 scopus 로고    scopus 로고
    • The evolution of travelling waves in fractional order autocatalysis with decay. I. Permanent form travelling waves
    • McCabe P.M., Leach J.A., Needham D.J., The evolution of travelling waves in fractional order autocatalysis with decay. I. Permanent form travelling waves. SIAM J. Appl. Math. 59:1998;870-899.
    • (1998) SIAM J. Appl. Math. , vol.59 , pp. 870-899
    • McCabe, P.M.1    Leach, J.A.2    Needham, D.J.3
  • 12
    • 0033651724 scopus 로고    scopus 로고
    • The evolution of travelling waves in fractional order autocatalysis with decay. II. The initial boundary value problem
    • McCabe P.M., Leach J.A., Needham D.J., The evolution of travelling waves in fractional order autocatalysis with decay. II. The initial boundary value problem. SIAM J. Appl. Math. 60:2000;1707-1748.
    • (2000) SIAM J. Appl. Math. , vol.60 , pp. 1707-1748
    • McCabe, P.M.1    Leach, J.A.2    Needham, D.J.3
  • 13
    • 0000151601 scopus 로고
    • The development of travelling waves in a simple isothermal chemical system. II. Cubic autocatalysis and linear decay
    • Merkin J.H., Needham D.J., The development of travelling waves in a simple isothermal chemical system. II. Cubic autocatalysis and linear decay. Proc. Roy. Soc. Lond. A. 430:1990;315-345.
    • (1990) Proc. Roy. Soc. Lond. A , vol.430 , pp. 315-345
    • Merkin, J.H.1    Needham, D.J.2
  • 14
    • 0011528276 scopus 로고
    • The development of travelling waves in a simple isothermal chemical system. IV. Quadratic autocatalysis with quadratic decay
    • Merkin J.H., Needham D.J., The development of travelling waves in a simple isothermal chemical system. IV. Quadratic autocatalysis with quadratic decay. Proc. Roy. Soc. Lond. A. 434:1990;531-554.
    • (1990) Proc. Roy. Soc. Lond. A , vol.434 , pp. 531-554
    • Merkin, J.H.1    Needham, D.J.2
  • 15
    • 0000321384 scopus 로고
    • Reaction-diffusion waves in an isothermal chemical system with general orders of autocatalysis and spatial dimension
    • Merkin J.H., Needham D.J., Reaction-diffusion waves in an isothermal chemical system with general orders of autocatalysis and spatial dimension. J. Appl. Math. Phys. (ZAMP) A. 44:1993;707-721.
    • (1993) J. Appl. Math. Phys. (ZAMP) A , vol.44 , pp. 707-721
    • Merkin, J.H.1    Needham, D.J.2
  • 16
    • 0001118302 scopus 로고
    • The development of travelling waves in a simple isothermal chemical system. I. Quadratic autocatalysis with linear decay
    • Merkin J.H., Needham D.J., Scott S.K., The development of travelling waves in a simple isothermal chemical system. I. Quadratic autocatalysis with linear decay. Proc. Roy. Soc. Lond. A. 424:1989;187-209.
    • (1989) Proc. Roy. Soc. Lond. A , vol.424 , pp. 187-209
    • Merkin, J.H.1    Needham, D.J.2    Scott, S.K.3
  • 17
    • 0035400209 scopus 로고    scopus 로고
    • Travelling spike autosolutions in the Gray-Scott model
    • Muratov C.B., Osipov V.V., Travelling spike autosolutions in the Gray-Scott model. Physica D. 155:2001;112-131.
    • (2001) Physica D , vol.155 , pp. 112-131
    • Muratov, C.B.1    Osipov, V.V.2
  • 19
    • 0011590802 scopus 로고
    • The development of travelling waves in a simple isothermal chemical system with general orders of autocatalysis and decay
    • Needham D.J., Merkin J.H., The development of travelling waves in a simple isothermal chemical system with general orders of autocatalysis and decay. Phil. Trans. Roy. Soc. Lond. 337:1991;261-274.
    • (1991) Phil. Trans. Roy. Soc. Lond. , vol.337 , pp. 261-274
    • Needham, D.J.1    Merkin, J.H.2
  • 20
    • 0347038753 scopus 로고    scopus 로고
    • A skeleton structure of self-replicating dynamics
    • Nishiura Y., Ueyama D., A skeleton structure of self-replicating dynamics. Physcia D. 130:1999;73-104.
    • (1999) Physcia D , vol.130 , pp. 73-104
    • Nishiura, Y.1    Ueyama, D.2
  • 21
    • 0000219822 scopus 로고
    • Exotic behavior of chemical reaction systems
    • Póta G., Stedman G., Exotic behavior of chemical reaction systems. Acta. Chim. Acad. Sci. Hung. 131:1994;229-268.
    • (1994) Acta. Chim. Acad. Sci. Hung. , vol.131 , pp. 229-268
    • Póta, G.1    Stedman, G.2
  • 22
    • 0000838693 scopus 로고    scopus 로고
    • Self-replicating spots in reaction-diffusion systems
    • Reynolds W.N., Ponce-Dawson S., Pearson J.E., Self-replicating spots in reaction-diffusion systems. Phys. Rev. E. 56:1997;185-198.
    • (1997) Phys. Rev. E , vol.56 , pp. 185-198
    • Reynolds, W.N.1    Ponce-Dawson, S.2    Pearson, J.E.3
  • 23
    • 0002011401 scopus 로고
    • The chemical basis of morphogenesis
    • Turing A.M., The chemical basis of morphogenesis. Phil. Trans. Roy. Soc. Lond. B. 237:1952;37-72.
    • (1952) Phil. Trans. Roy. Soc. Lond. B , vol.237 , pp. 37-72
    • Turing, A.M.1
  • 24
    • 0036067340 scopus 로고    scopus 로고
    • Asymmetric spike patterns for the one-dimensional Gierer-Meinhardt model: Equilibria and stability
    • Ward M.J., Wei J.C., Asymmetric spike patterns for the one-dimensional Gierer-Meinhardt model: equilibria and stability. Eur. J. Appl. Math. 13:2002;283-320.
    • (2002) Eur. J. Appl. Math. , vol.13 , pp. 283-320
    • Ward, M.J.1    Wei, J.C.2
  • 25
    • 0036809985 scopus 로고    scopus 로고
    • The existence and stability of asymmetric spike patterns for the Schnakenberg model
    • Ward M.J., Wei J.C., The existence and stability of asymmetric spike patterns for the Schnakenberg model. Stud. Appl. Math. 109:2002;229-264.
    • (2002) Stud. Appl. Math. , vol.109 , pp. 229-264
    • Ward, M.J.1    Wei, J.C.2
  • 26
    • 0003077491 scopus 로고    scopus 로고
    • Pattern formations in two-dimensional Gray-Scott model: Existence of single-spot solutions and their stabilit
    • Wei J.C., Pattern formations in two-dimensional Gray-Scott model: existence of single-spot solutions and their stabilit. Physica D. 148:2001;20-48.
    • (2001) Physica D , vol.148 , pp. 20-48
    • Wei, J.C.1
  • 27
    • 0033414750 scopus 로고    scopus 로고
    • On single interior spike solutions of Gierer-Meinhardt system: Uniqueness, spectrum estimates and stability analysis
    • Wei J.C., On single interior spike solutions of Gierer-Meinhardt system: uniqueness, spectrum estimates and stability analysis. Eur. J. Appl. Math. 10:1999;353-378.
    • (1999) Eur. J. Appl. Math. , vol.10 , pp. 353-378
    • Wei, J.C.1
  • 28
    • 0033130430 scopus 로고    scopus 로고
    • Existence, stability and metastability of point condensation patterns generated by the Gray-Scott system
    • Wei J.C., Existence, stability and metastability of point condensation patterns generated by the Gray-Scott system. Nonlinearity. 12:1999;593-616.
    • (1999) Nonlinearity , vol.12 , pp. 593-616
    • Wei, J.C.1
  • 29
    • 0038552816 scopus 로고    scopus 로고
    • On a hypercycle system with nonlinear rate
    • Wei J.C., Winter M., On a hypercycle system with nonlinear rate. Meth. Appl. Anal. 8:2001;257-278.
    • (2001) Meth. Appl. Anal. , vol.8 , pp. 257-278
    • Wei, J.C.1    Winter, M.2
  • 31
    • 0034311523 scopus 로고    scopus 로고
    • On a two-dimensional reaction-diffusion system with hypercyclical structure
    • Wei J.C., Winter M., On a two-dimensional reaction-diffusion system with hypercyclical structure. Nonlinearity. 13:2000;2005-2032.
    • (2000) Nonlinearity , vol.13 , pp. 2005-2032
    • Wei, J.C.1    Winter, M.2
  • 32
    • 0038213974 scopus 로고    scopus 로고
    • A nonloal eigenvalue problem and the stability of spikes for reaction-diffusion systems with fractional reaction rates
    • in press
    • J.C. Wei, M. Winter, A nonloal eigenvalue problem and the stability of spikes for reaction-diffusion systems with fractional reaction rates, Int. J. Bifur. Chaos, in press.
    • Int. J. Bifur. Chaos
    • Wei, J.C.1    Winter, M.2


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