Modeling of Turing Structures in the Chlorite—Iodide—Malonic Acid—Starch Reaction System

Recent experiments on the chlorite-iodide-malonic acid-starch reaction in a gel reactor give the first evidence of the existence of the symmetry breaking, reaction-diffusion structures predicted by Turing in 1952. A five-variable model that describes the temporal behavior of the system is reduced to a two-variable model, and its spatial behavior is analyzed. Structures have been found with wavelengths that are in good agreement with those observed experimentally. The gel plays a key role by binding key iodine species, thereby creating the necessary difference in the effective diffusion coefficients of the activator and inhibitor species, iodide and chlorite ions, respectively.

[1]  J. Murray A Pre-pattern formation mechanism for animal coat markings , 1981 .

[2]  V. Fairén,et al.  Stability diagram and nonlinear structures in a simple reaction scheme involving inhibition forward , 1976 .

[3]  R. L. Pecsok,et al.  Calculation of distribution coefficients in inorganic gel chromatography , 1968 .

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

[5]  J. Henderson Numerical Experiments on Continental Lithosphere Extension Department of Earth and Planetary Sciences , 2022 .

[6]  Turing bifurcation and stationary patterns in the ferroin-catalyzed Belousov-Zhabotinskii reaction , 1987 .

[7]  J. Pearson,et al.  Turing instabilities with nearly equal diffusion coefficients , 1989 .

[8]  Daniel R. Ripoll,et al.  Molecular model of the cooperative amylose-iodine-triiodide complex , 1986 .

[9]  I. Ruff,et al.  Transfer diffusion. III. Kinetics and mechanism of the triiodide-iodide exchange reaction , 1972 .

[10]  Grégoire Nicolis,et al.  Self-Organization in nonequilibrium systems , 1977 .

[11]  A. Turing The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[12]  C. Berding On the heterogeneity of reaction-diffusion generated pattern , 1987, Bulletin of mathematical biology.

[13]  J. Murray,et al.  Parameter space for turing instability in reaction diffusion mechanisms: a comparison of models. , 1982, Journal of theoretical biology.

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

[15]  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 .

[16]  Chang-Hwan Kim,et al.  Iodine Catalysis in the Chlorite-Iodide Reaction1 , 1965 .

[17]  D. Harrison,et al.  Theory of oscillations of respiration rate in continuous culture of Klebsiella aerogenes. , 1969, Journal of theoretical biology.