Computer simulation of Turing structures in the chlorite-iodide-malonic acid system

The emergence, growth and stabilization of stationary concentration patterns in a continuously fed chemical reaction-diffusion system are studied through numerical simulation of the Lengyel-Epstein model. This model represents a key to understanding the recently obtained Turing structures in the chlorite-iodide-malonic acid system. Using the supply of iodine as a control parameter, the regularity of the hexagonal patterns that develop from the noise inflicted homogeneous steady state is examined. In the region where they are both stable, the competition between Hopf oscillations and Turing stripes is studied by following the propagation of a front connecting the two modes. Finally, examples are given for the types of structures that can develop when a gradient in feed concentration is applied to the system.

[1]  H. Swinney,et al.  Sustained chemical waves in an annular gel reactor: a chemical pinwheel , 1987, Nature.

[2]  J. Murray,et al.  On pattern formation mechanisms for lepidopteran wing patterns and mammalian coat markings. , 1981, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[3]  G. Dewel,et al.  Fluctuations near nonequilibrium phase transitions to nonuniform states , 1980 .

[4]  D. Clapham,et al.  Spiral calcium wave propagation and annihilation in Xenopus laevis oocytes. , 1991, Science.

[5]  Ole Jensen,et al.  Subcritical transitions to Turing structures , 1993 .

[6]  Dulos,et al.  Experimental evidence of a sustained standing Turing-type nonequilibrium chemical pattern. , 1990, Physical review letters.

[7]  G. Dewel,et al.  Reentrant hexagonal Turing structures , 1992 .

[8]  Irving R. Epstein,et al.  Experimental and modeling study of oscillations in the chlorine dioxide-iodine-malonic acid reaction , 1990 .

[9]  Irving R. Epstein,et al.  Systematic design of chemical oscillators. Part 65. Batch oscillation in the reaction of chlorine dioxide with iodine and malonic acid , 1990 .

[10]  E. Dulos,et al.  Turing Patterns in Confined Gel and Gel-Free Media , 1992 .

[11]  Axel Hunding,et al.  Size adaptation of turing prepatterns , 1988, Journal of mathematical biology.

[12]  Harry L. Swinney,et al.  Hydrodynamic instabilities and the transition to turbulence , 1981 .

[13]  H. Meinhardt.  Models of biological pattern formation , 1982 .

[14]  R. D. Vigil,et al.  Turing patterns in a simple gel reactor , 1992 .

[15]  J. Boissonade,et al.  Numerical studies of Turing patterns selection in a two-dimensional system , 1992 .

[16]  L. Wolpert.  Positional information and pattern formation. , 1981, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[17]  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.

[18]  H. Swinney,et al.  Transition from a uniform state to hexagonal and striped Turing patterns , 1991, Nature.

[19]  J. Boissonade,et al.  Conventional and unconventional Turing patterns , 1992 .

[20]  L. Wolpert.  Positional information and the spatial pattern of cellular differentiation. , 1969, Journal of theoretical biology.

[21]  R. J. Field,et al.  The evolution of patterns in a homogeneously oscillating medium , 1992 .

[22]  A. Winfree.  Spiral Waves of Chemical Activity , 1972, Science.

[23]  I. Prigogine,et al.  On symmetry-breaking instabilities in dissipative systems , 1967 .

[24]  Jensen,et al.  Localized structures and front propagation in the Lengyel-Epstein model. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[25]  Y. Pomeau.  Front motion, metastability and subcritical bifurcations in hydrodynamics , 1986 .

[26]  Gregor Eichele,et al.  Identification and spatial distribution of retinoids in the developing chick limb bud , 1987, Nature.

[27]  Guy Dewel,et al.  Three-dimensional dissipative structures in reaction-diffusion systems , 1992 .

[28]  E. Mosekilde,et al.  Transient current decay in semiconducting ZnO due to the acousto - electric effect , 1967 .

[29]  Guy Dewel,et al.  Competition in ramped Turing structures , 1992 .

[30]  Perraud,et al.  One-dimensional "spirals": Novel asynchronous chemical wave sources. , 1993, Physical review letters.