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Volumn 114, Issue 2, 2005, Pages 115-165

Pulse-splitting for some reaction-diffusion systems in one-space dimension

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION IN LIQUIDS; PERTURBATION TECHNIQUES;

EID: 12844286218     PISSN: 00222526     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.0022-2526.2005.01542.x     Document Type: Article
Times cited : (16)

References (43)
  • 2
    • 84968466504 scopus 로고
    • Collocation software for boundary value ODE's
    • U. ASCHER, R. CHRISTIANSEN, and R. RUSSELL, Collocation software for boundary value ODE's, Math. Comp. 33:659-679 (1979).
    • (1979) Math. Comp. , vol.33 , pp. 659-679
    • Ascher, U.1    Christiansen, R.2    Russell, R.3
  • 3
    • 23044530537 scopus 로고    scopus 로고
    • The Gierer Meinhardt system: The breaking of homoclinics and multi-bump ground states
    • M. DEL PINO, M. KOWALCZYK, and X. CHEN, The Gierer Meinhardt system: the breaking of homoclinics and multi-bump ground states, Commun. Contemp. Math. 3(3):419-439 (2001).
    • (2001) Commun. Contemp. Math. , vol.3 , Issue.3 , pp. 419-439
    • Del Pino, M.1    Kowalczyk, M.2    Chen, X.3
  • 4
    • 0034912344 scopus 로고    scopus 로고
    • Slowly modulated two-pulse solutions in the gray-scott model I: Asymptotic construction and stability
    • A. DOELMAN, W. ECKHAUS, and T. J. KAPER, Slowly modulated two-pulse solutions in the Gray-Scott model I: asymptotic construction and stability, SIAM J. Appl. Math. 61(3): 1080-1102 (2000).
    • (2000) SIAM J. Appl. Math. , vol.61 , Issue.3 , pp. 1080-1102
    • Doelman, A.1    Eckhaus, W.2    Kaper, T.J.3
  • 5
    • 0035704463 scopus 로고    scopus 로고
    • Slowly modulated two-pulse solutions in the Gray-Scott model II: Geometric theory, bifurcations, and splitting dynamics
    • A. DOELMAN, W. ECKHAUS, and T. J. KAPER, Slowly modulated two-pulse solutions in the Gray-Scott model II: geometric theory, bifurcations, and splitting dynamics, SIAM J. Appl. Math. 61(6): 2036-2061 (2000).
    • (2000) SIAM J. Appl. Math. , vol.61 , Issue.6 , pp. 2036-2061
    • Doelman, A.1    Eckhaus, W.2    Kaper, T.J.3
  • 6
    • 0005468518 scopus 로고    scopus 로고
    • Stability analysis of singular patterns in the 1D gray-scott model: A matched asymptotics approach
    • A. DOELMAN, R. A. GARDNER, and T. J. KAPER, Stability analysis of singular patterns in the 1D Gray-Scott model: a matched asymptotics approach, Physica D 122:1-36 (1998).
    • (1998) Physica D , vol.122 , pp. 1-36
    • Doelman, A.1    Gardner, R.A.2    Kaper, T.J.3
  • 7
    • 85087535076 scopus 로고    scopus 로고
    • A stability index analysis of 1-D patterns of the Gray-Scott model
    • A. DOELMAN, R. A. GARDNER, and T. KAPER, A stability index analysis of 1-D patterns of the Gray-Scott model, Memoirs of AMS 155(737): (2002).
    • (2002) Memoirs of AMS , vol.155 , Issue.737
    • Doelman, A.1    Gardner, R.A.2    Kaper, T.3
  • 8
    • 0000132086 scopus 로고    scopus 로고
    • Large stable pulse solutions in reaction-diffusion equations
    • A. DOELMAN, R. A. GARDNER, and T. KAPER, Large stable pulse solutions in reaction-diffusion equations, Indiana U. Math. J. 50(1):443-507 (2001).
    • (2001) Indiana U. Math. J. , vol.50 , Issue.1 , pp. 443-507
    • Doelman, A.1    Gardner, R.A.2    Kaper, T.3
  • 9
    • 0000706319 scopus 로고    scopus 로고
    • Pattern formation in the one-dimensional gray-scott model
    • A. DOELMAN, T. J. KAPER, and P. ZEGELING, Pattern formation in the one-dimensional Gray-Scott model, Nonlinearity 10:523-563 (1997).
    • (1997) Nonlinearity , vol.10 , pp. 523-563
    • Doelman, A.1    Kaper, T.J.2    Zegeling, P.3
  • 11
    • 0347670293 scopus 로고    scopus 로고
    • n Splitting or edge splitting?: A manner of splitting in dissipative systems
    • n Splitting or edge splitting?: a manner of splitting in dissipative systems, Jpn. J. Indust. Appl. Math. 18:181-205 (2001).
    • (2001) Jpn. J. Indust. Appl. Math. , vol.18 , pp. 181-205
    • Ei, S.1    Nishiura, Y.2    Ueda, K.3
  • 12
    • 12844276566 scopus 로고
    • Slow passage through bifurcation and limit points. Afsymptotic theory and applications
    • Dynamic Bifurcations (Luminy 1990), Springer, Berlin
    • T. ERNEUX, E. L. REISS, L. J. HOLDEN, and M. GEORGIOU, Slow passage through bifurcation and limit points. asymptotic theory and applications, Dynamic Bifurcations (Luminy 1990), 14-28, Lecture Notes in Math., 1493, Springer, Berlin (1991).
    • (1991) Lecture Notes in Math. , vol.1493 , pp. 14-28
    • Erneux, T.1    Reiss, E.L.2    Holden, L.J.3    Georgiou, M.4
  • 13
    • 0015454185 scopus 로고
    • A theory of biological pattern formation
    • 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
  • 14
    • 0031207358 scopus 로고    scopus 로고
    • Dynamical hysteresis without static hysteresis: Scaling laws and asymptotic expansions
    • G. GOLDSZTEIN, F. BRONER, and S. H. STROGATZ, Dynamical hysteresis without static hysteresis: scaling laws and asymptotic expansions, SIAM J. Appl. Math. 57(4): 1163-1187 (1997).
    • (1997) SIAM J. Appl. Math. , vol.57 , Issue.4 , pp. 1163-1187
    • Goldsztein, G.1    Broner, F.2    Strogatz, S.H.3
  • 15
    • 0021310291 scopus 로고
    • Autocatalytic reactions in the isothermal, continuous stirred tank reactor: Oscillations and instabilities in the system a + 2B → 3B, B → C
    • P. GRAY and S. K. SCOTT, Autocatalytic reactions in the isothermal, continuous stirred tank reactor: oscillations and instabilities in the system A + 2B → 3B, B → C, Chem. Eng. Sci. 39:1087-1097 (1984).
    • (1984) Chem. Eng. Sci. , vol.39 , pp. 1087-1097
    • Gray, P.1    Scott, S.K.2
  • 16
    • 0035277877 scopus 로고    scopus 로고
    • The stability of spike solutions to the one-dimensional Gierer-Meinhardt model
    • D. IRON, M. J. WARD, and J. WEI, The stability of spike solutions to the one-dimensional Gierer-Meinhardt model, Physica D 150(1-2):25-62 (2001).
    • (2001) Physica D , vol.150 , Issue.1-2 , pp. 25-62
    • Iron, D.1    Ward, M.J.2    Wei, J.3
  • 17
    • 0036665085 scopus 로고    scopus 로고
    • The dynamics of multi-spike solutions to the one-dimensional Gierer-Meinhardt model
    • D. IRON and M. J. WARD, The dynamics of multi-spike solutions to the one-dimensional Gierer-Meinhardt model, SIAM J. Appl. Math. 62(6):1924-1951 (2002).
    • (2002) SIAM J. Appl. Math. , vol.62 , Issue.6 , pp. 1924-1951
    • Iron, D.1    Ward, M.J.2
  • 18
    • 0003394350 scopus 로고
    • Tata Institute of Fundamental Research Lectures on Mathematics and Physics Tata Institute, Bombay, by Springer-Verlag, Berlin
    • H. B. KELLER, Lectures on Numerical Methods in Bifurcation Problems, Tata Institute of Fundamental Research Lectures on Mathematics and Physics 79, Tata Institute, Bombay, by Springer-Verlag, Berlin, (1987).
    • (1987) Lectures on Numerical Methods in Bifurcation Problems , vol.79
    • Keller, H.B.1
  • 19
    • 85153177023 scopus 로고    scopus 로고
    • The existence and stability of spike equilibria in the one-dimensional gray-scott model
    • submitted
    • T. KOLOKOLNIKOV, M. WARD, and J. WEI, The existence and stability of spike equilibria in the one-dimensional Gray-Scott model, Studies in Appl. Math., submitted.
    • Studies in Appl. Math.
    • Kolokolnikov, T.1    Ward, M.2    Wei, J.3
  • 20
    • 12844286906 scopus 로고    scopus 로고
    • The stability of spike equilibria in the one-dimensional Gray-Scott model: The pulse-splitting regime
    • submitted
    • T. KOLOKOLNIKOV, M. WARD, and J. WEI, The stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime, submitted, Physica D, (2003).
    • (2003) Physica D
    • Kolokolnikov, T.1    Ward, M.2    Wei, J.3
  • 21
    • 0028242433 scopus 로고
    • Experimental observation of self-replicating spots in a reaction-diffusion system
    • K. J. LEE, W. D. MCCORMICK, J. E. PEARSON, and H. L. SWINNEY, Experimental observation of self-replicating spots in a reaction-diffusion system, Nature 369:215-218 (1994).
    • (1994) Nature , vol.369 , pp. 215-218
    • Lee, K.J.1    Mccormick, W.D.2    Pearson, J.E.3    Swinney, H.L.4
  • 22
    • 0002542873 scopus 로고
    • Large amplitude stationary solutions to a chemotaxis system
    • C. S. LIN, W. M. NI, and I. TAKAGI, Large amplitude stationary solutions to a chemotaxis system, J. Diff. Eq. 72(1):1-27 (1988).
    • (1988) J. Diff. Eq. , vol.72 , Issue.1 , pp. 1-27
    • Lin, C.S.1    Ni, W.M.2    Takagi, I.3
  • 23
    • 0034215317 scopus 로고    scopus 로고
    • Pattern formation with a conservation Law
    • P. C. MATTHEWS and S. M. COX, Pattern formation with a conservation Law, Nonlinearity 13(4): 1293-1320 (2000).
    • (2000) Nonlinearity , vol.13 , Issue.4 , pp. 1293-1320
    • Matthews, P.C.1    Cox, S.M.2
  • 26
    • 0035400209 scopus 로고    scopus 로고
    • Traveling spike auto-solitons in the gray-scott model
    • C. MURATOV and V. V. OSIPOV, Traveling spike auto-solitons in the Gray-Scott model, Physica D 155(1-2):112-131 (2001).
    • (2001) Physica D , vol.155 , Issue.1-2 , pp. 112-131
    • Muratov, C.1    Osipov, V.V.2
  • 27
    • 0036588860 scopus 로고    scopus 로고
    • Stability of the static spike autosolitons in the gray-scott model
    • C. MURATOV and V. V. OSIPOV, Stability of the static spike autosolitons in the Gray-Scott model, SIAM J. Appl. Math. 62(5): 1463-1487 (2002).
    • (2002) SIAM J. Appl. Math. , vol.62 , Issue.5 , pp. 1463-1487
    • Muratov, C.1    Osipov, V.V.2
  • 28
    • 0034623753 scopus 로고    scopus 로고
    • Static spike autosolitons in the Gray-Scott model
    • C. MURATOV and V. V. OSIPOV, Static spike autosolitons in the Gray-Scott model, J. Phys. A: Math Gen. 33:8893-8916 (2000).
    • (2000) J. Phys. A: Math Gen. , vol.33 , pp. 8893-8916
    • Muratov, C.1    Osipov, V.V.2
  • 29
    • 0004332272 scopus 로고
    • routine D03PCF, Numerical Algorithms Group Ltd., Oxford, United Kingdom
    • NAG Fortran library Mark 17, routine D03PCF, Numerical Algorithms Group Ltd., Oxford, United Kingdom (1995).
    • (1995) NAG Fortran Library Mark , vol.17
  • 30
    • 0142078631 scopus 로고    scopus 로고
    • Translations of Mathematical Monographs, AMS publications, Providence, Rhode Island
    • Y. NISHIURA, Far-From-Equilibrium Dynamics, Translations of Mathematical Monographs, Vol. 209, AMS publications, Providence, Rhode Island, (2002).
    • (2002) Far-from-equilibrium Dynamics , vol.209
    • Nishiura, Y.1
  • 31
    • 0347038753 scopus 로고    scopus 로고
    • A skeleton structure of self-replicating dynamics
    • Y. NISHIURA and D. UEYAMA, A skeleton structure of self-replicating dynamics, Physica D 130:73-104 (1999).
    • (1999) Physica D , vol.130 , pp. 73-104
    • Nishiura, Y.1    Ueyama, D.2
  • 32
    • 0035311814 scopus 로고    scopus 로고
    • Spatial-temporal chaos for the gray-scott model
    • Y. NISHIURA and D. UEYAMA, Spatial-temporal chaos for the Gray-Scott model, Physica D 150:137-162 (2001).
    • (2001) Physica D , vol.150 , pp. 137-162
    • Nishiura, Y.1    Ueyama, D.2
  • 33
    • 0041471616 scopus 로고    scopus 로고
    • Existence and stability of singular patterns in a Ginzburg-Landau equation coupled with a mean field
    • J. NORBURY, J. WEI, and M. WINTER, Existence and stability of singular patterns in a Ginzburg-Landau equation coupled with a mean field, Nonlinearity 15(6):2077-2096 (2002).
    • (2002) Nonlinearity , vol.15 , Issue.6 , pp. 2077-2096
    • Norbury, J.1    Wei, J.2    Winter, M.3
  • 34
    • 0001102631 scopus 로고
    • Complex patterns in a simple system
    • J. E. PEARSON, Complex patterns in a simple system, Science 216:189-192 (1993).
    • (1993) Science , vol.216 , pp. 189-192
    • Pearson, J.E.1
  • 35
    • 0030101235 scopus 로고
    • Excitability, wave reflection, and wave splitting in a cubic autocatalysis reaction-diffusion system
    • V. PETROV, S. K. SCOTT, and K. SHOWALTER, Excitability, wave reflection, and wave splitting in a cubic autocatalysis reaction-diffusion system, Phil. Trans. Roy. Soc. London, Series A 347:631-642 (1994).
    • (1994) Phil. Trans. Roy. Soc. London, Series A , vol.347 , pp. 631-642
    • Petrov, V.1    Scott, S.K.2    Showalter, K.3
  • 36
    • 0001360757 scopus 로고
    • Dynamics of self-replicating patterns in reaction-diffusion systems
    • W. N. REYNOLDS, S. PONCE-DAWSON, and J. E. PEARSON, Dynamics of self-replicating patterns in reaction-diffusion systems, Phys. Rev. Lett. 72:2797-2800 (1994).
    • (1994) Phys. Rev. Lett. , vol.72 , pp. 2797-2800
    • Reynolds, W.N.1    Ponce-Dawson, S.2    Pearson, J.E.3
  • 37
    • 0000838693 scopus 로고    scopus 로고
    • Dynamics of self-replicating spots in reaction-diffusion systems
    • W. N. REYNOLDS, S. PONCE-DAWSON, and J. E. PEARSON, Dynamics of self-replicating spots in reaction-diffusion systems, Phys. Rev. E 56(1): 185-198 (1997).
    • (1997) Phys. Rev. E , vol.56 , Issue.1 , pp. 185-198
    • Reynolds, W.N.1    Ponce-Dawson, S.2    Pearson, J.E.3
  • 38
    • 0001148075 scopus 로고
    • Coexisting pulses in a model for binary-mixture convection
    • H. RIECKE and W. J. RAPPEL, Coexisting pulses in a model for binary-mixture convection, Phys. Rev. Lett. 75:4035-4038 (1995).
    • (1995) Phys. Rev. Lett. , vol.75 , pp. 4035-4038
    • Riecke, H.1    Rappel, W.J.2
  • 39
    • 0141646882 scopus 로고    scopus 로고
    • Numerical challenges for resolving spike dynamics for two reaction-diffusion systems
    • W. SUN, T. TANG, M. J. WARD, and J. WEI, Numerical challenges for resolving spike dynamics for two reaction-diffusion systems, Studies in Appl. Math. 111:41-84 (2003).
    • (2003) Studies in Appl. Math. , vol.111 , pp. 41-84
    • Sun, W.1    Tang, T.2    Ward, M.J.3    Wei, J.4
  • 40
    • 0012011523 scopus 로고    scopus 로고
    • Dynamics of self-replicating patterns in the one-dimensional gray-scott model
    • D. UEYAMA, Dynamics of self-replicating patterns in the one-dimensional Gray-Scott model, Hokkaido Math J. 28(1): 175-210 (1999).
    • (1999) Hokkaido Math J. , vol.28 , Issue.1 , pp. 175-210
    • Ueyama, D.1
  • 41
    • 84867997764 scopus 로고    scopus 로고
    • Hopf bifurcations and oscillatory instabilities of spike solutions for the one-dimensional gierer-meinhardt model
    • M. J. WARD and J. WEI, Hopf bifurcations and oscillatory instabilities of spike solutions for the one-dimensional Gierer-Meinhardt model, J. Nonlinear Sci. 13(2):209-264 (2003).
    • (2003) J. Nonlinear Sci. , vol.13 , Issue.2 , pp. 209-264
    • Ward, M.J.1    Wei, J.2
  • 42
    • 0033414750 scopus 로고    scopus 로고
    • On single interior spike solutions for the gierer-meinhardt system: Uniqueness and stability estimates
    • J. WEI, On single interior spike solutions for the Gierer-Meinhardt system: uniqueness and stability estimates, Euro. J. Appl. Math. 10(4):353-378 (1999).
    • (1999) Euro. J. Appl. Math. , vol.10 , Issue.4 , pp. 353-378
    • Wei, J.1
  • 43
    • 85153230204 scopus 로고    scopus 로고
    • On a cubic-quintic ginzburg-landau equation with global coupling
    • to appear
    • J. WEI and M. WINTER, On a cubic-quintic Ginzburg-Landau equation with global coupling, Proc. Amer. Math. Soc. (2004) to appear.
    • (2004) Proc. Amer. Math. Soc.
    • Wei, J.1    Winter, M.2


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