Turing Pattern Formation in the Brusselator Model with Superdiffusion
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Bernard J. Matkowsky | Vladimir A. Volpert | Alexander A. Golovin | B. Matkowsky | A. Golovin | V. Volpert
[1] Bruce Ian Henry,et al. Turing pattern formation with fractional diffusion and fractional reactions , 2007 .
[2] Santos B. Yuste,et al. Subdiffusion-limited A+A reactions. , 2001 .
[3] Laurent Seuront,et al. Multifractal random walk in copepod behavior , 2001 .
[4] S L Wearne,et al. Turing pattern formation in fractional activator-inhibitor systems. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.
[5] A. M. Zhabotinskii. [PERIODIC COURSE OF THE OXIDATION OF MALONIC ACID IN A SOLUTION (STUDIES ON THE KINETICS OF BEOLUSOV'S REACTION)]. , 1964, Biofizika.
[6] H. Habersack,et al. On bed particle diffusion in gravel bed flows under weak bed load transport , 2002 .
[7] H. Haken. Synergetics: an Introduction, Nonequilibrium Phase Transitions and Self-organization in Physics, Chemistry, and Biology , 1977 .
[8] V. Vanag. Waves and patterns in reaction-diffusion systems. Belousov-Zhabotinsky reaction in water-in-oil microemulsions , 2004 .
[9] Paul C. Fife,et al. Mathematical Aspects of Reacting and Diffusing Systems , 1979 .
[10] Lopez,et al. Multifractal structure of chaotically advected chemical fields , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[11] Joseph W. Haus,et al. Diffusion in regular and disordered lattices , 1987 .
[12] G. Schatz,et al. Anomalous surface diffusion in nanoscale direct deposition processes. , 2003, Physical review letters.
[13] Vladimir K. Vanag,et al. Asymmetrical Concentration Fluctuations in the Autocatalytic Bromate-Bromide-Catalyst Reaction and in the Oscillatory Belousov- Zhabotinsky Reaction in Closed Reactor: Stirring Effects , 1995 .
[14] Z. Wlodarczyk,et al. Do we observe levy flights in cosmic rays , 1999 .
[15] Vickie E. Lynch,et al. Anomalous diffusion and exit time distribution of particle tracers in plasma turbulence model , 2001 .
[16] J. Toner,et al. Hydrodynamics and phases of flocks , 2005 .
[17] H. Swinney,et al. Transition from a uniform state to hexagonal and striped Turing patterns , 1991, Nature.
[18] Katja Lindenberg,et al. Reaction front in an A+B-->C reaction-subdiffusion process. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.
[19] Daniel Walgraef,et al. Spatio-temporal pattern formation , 1996 .
[20] A. M. Turing,et al. The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.
[21] Zoltán Noszticzius,et al. Hydrodynamic turbulence and diffusion-controlled reactions. Simulation of the effect of stirring on the oscillating Belousov-Zhabotinsky reaction with the radicalator model , 1991 .
[22] Bruce Ian Henry,et al. Existence of Turing Instabilities in a Two-Species Fractional Reaction-Diffusion System , 2002, SIAM J. Appl. Math..
[23] I. Epstein,et al. A chemical approach to designing Turing patterns in reaction-diffusion systems. , 1992, Proceedings of the National Academy of Sciences of the United States of America.
[24] R. Hilfer. Applications Of Fractional Calculus In Physics , 2000 .
[25] Jichang Wang,et al. Stirring-controlled bifurcations in the 1,4-cyclohexanedione-bromate reaction. , 2005, The journal of physical chemistry. A.
[26] Michael Menzinger,et al. Heterogeneities and stirring effects in the Belusov-Zhabotinskii reaction , 1986 .
[27] Matthias Weiss,et al. Stabilizing Turing patterns with subdiffusion in systems with low particle numbers. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.
[28] P. A. Prince,et al. Lévy flight search patterns of wandering albatrosses , 1996, Nature.
[29] I. Epstein,et al. Modeling of Turing Structures in the Chlorite—Iodide—Malonic Acid—Starch Reaction System , 1991, Science.
[30] Peter Ruoff. Excitations induced by fluctuations: an explanation of stirring effects and chaos in closed anaerobic classical Belousov-Zhabotinskii systems , 1993 .
[31] V E Lynch,et al. Front dynamics in reaction-diffusion systems with Levy flights: a fractional diffusion approach. , 2002, Physical review letters.
[32] Irving R. Epstein,et al. Stirring and premixing effects in the oscillatory chlorite–iodide reaction , 1986 .
[33] J Langowski,et al. Anomalous diffusion of fluorescent probes inside living cell nuclei investigated by spatially-resolved fluorescence correlation spectroscopy. , 2000, Journal of molecular biology.
[34] Baowen Li,et al. Anomalous heat conduction and anomalous diffusion in one-dimensional systems. , 2003, Physical review letters.
[35] Kenneth Showalter,et al. Control of waves, patterns and turbulence in chemical systems , 2006 .
[36] J. Bouchaud,et al. Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications , 1990 .
[37] Tommy Nilsson,et al. Anomalous protein diffusion in living cells as seen by fluorescence correlation spectroscopy. , 2003, Biophysical journal.
[38] 医療政策委員会. Concentration wave propagation in two-dimensional liquid-phase self-oscillating system , 1970 .
[39] Gerardo Palazzo,et al. Anomalous surfactant diffusion in a living polymer system. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.
[40] Alexander A. Nepomnyashchy,et al. Oscillatory instability in super-diffusive reaction – diffusion systems: Fractional amplitude and phase diffusion equations , 2008 .
[41] Tamás Tél,et al. Effective dimensions and chemical reactions in fluid flows. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.
[42] D. Brockmann,et al. Front Propagation in Reaction-Superdiffusion Dynamics: Taming Levy Flights with Fluctuations , 2004, cond-mat/0401322.
[43] J. Klafter,et al. The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .
[44] V. V. Gafiychuk,et al. Pattern formation in a fractional reaction diffusion system , 2006 .
[45] I M Sokolov,et al. Diffusion on a solid surface: anomalous is normal. , 2004, Physical review letters.
[46] D. Zanette,et al. Experimental evidence of power-law trapping-time distributions in porous media. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[47] A. Mikhailov. Foundations of Synergetics I: Distributed Active Systems , 1991 .
[48] Cristóbal López,et al. Excitable media in open and closed chaotic flows. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.
[49] Alex Hansen,et al. Two-dimensional turbulence and dispersion in a freely decaying system , 1998 .
[50] Solomon,et al. Observation of anomalous diffusion and Lévy flights in a two-dimensional rotating flow. , 1993, Physical review letters.
[51] J. Klafter,et al. The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics , 2004 .
[52] J. E. Pearson. Complex Patterns in a Simple System , 1993, Science.
[53] E. Montroll,et al. Anomalous transit-time dispersion in amorphous solids , 1975 .
[54] Maggs,et al. Subdiffusion and Anomalous Local Viscoelasticity in Actin Networks. , 1996, Physical review letters.
[55] N. Rashevsky,et al. Mathematical biology , 1961, Connecticut medicine.
[56] Angelo Vulpiani,et al. Superfast front propagation in reactive systems with non-Gaussian diffusion , 2002 .
[57] Yoshiki Kuramoto,et al. Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.
[58] N. Britton. Reaction-diffusion equations and their applications to biology. , 1989 .
[59] I M Sokolov,et al. Reaction-subdiffusion equations. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.
[60] K. Kaplan. H. Haken, Synergetics. An Introduction. Nonequilibrium Phase Transitions and Self-Organization in Physics, Chemistry, and Biology (2nd Edition). XI + 355 S., 152 Abb. Berlin—Heidelberg—New York 1978. Springer-Verlag. DM 66,00 , 1980 .
[61] Angelo Vulpiani,et al. Front propagation in reactive systems with anomalous diffusion , 2003 .
[62] A. Winfree. Spiral Waves of Chemical Activity , 1972, Science.