Experimental and quantitative modeling studies of Turing pattern formation under stochastic spatial fluctuations

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 11, Issue 11, 2001, Pages 2739-2749

  Sanz Anchelergues, Adolfo ^a   Muñuzuri, Alberto P ^a  

^a UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035515102     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127401003814     Document Type: Article

References (18)

1. Castets, V., Dulos, E., Boissonade, J. & DeKepper, P. [1990] "Experimental evidence of a sustained standing Turing-type nonequilibrium chemical pattern," Phys. Rev. Lett. 64, 2953-2956.
2. De Kepper, P., Epstein, I. R., Kustin, K. & Orbán, M. [1982] "Batch oscillations and spatial wave patterns in chlorite oscillating systems," J. Phys. Chem. 86, 170-171.
3. Hortváth, A., Dolnik, M., Muñuzuri, A. P., Zhabotinsky, A. M. & Epstein, I. R. [1999] "Control of Turing structures by periodic illumination," Phys. Rev. Lett. 83(15), 2950-2952.
4. Kapral, R. & Showalter, K. [1995] Chemical Waves and Patterns (Kluwer Academic Publishers, Amsterdam).
5. Kern, D. M. & Kim, C. H. [1965] "Iodine catalysis in the chlorite-iodide reaction," J. Am. Chem. Soc. 87, 5309-5313.
6. Koch, A. J. & Meinhardt, H. [1994] "Biological pattern formation: From basis mechanisms to complex structures," Rev. Mod. Phys. 66, 1481-1507.
7. Lengyel, I., Rabai, G. & Epstein, I. R. [1990a] "Batch oscillation in the reaction of chlorine dioxide with iodine and malonic acid," J. Am. Chem. Soc. 112, 4606-4607.
8. Lengyel, I., Rabai, G. & Epstein, I. R. [1990b] "Experimental and modeling study of oscillations in the chlorine dioxide-iodine-malonic acid reaction," J. Am. Chem. Soc. 112, 9104-9110.
9. Lengyel, I. & Epstein, I. R. [1991] "Modeling of Turing structures in the chlorite-iodide-malonic acid-it starch reaction system," Science 251, 650-652.
10. Lengyel, I. & Epstein, I. R. [1995] "The chemistry behind the first experimental chemical examples of Turing patterns," in Chemical Waves and Patterns, eds. Kapral, R. & Showalter, K. (Klüwer Academic Publishers, Amsterdam), pp. 297-322.
11. Meinhardt, H. [1982] Models of Biological Pattern Formation (Academic Press, London).
12. Muñuzuri, A. P., Dolnik, M., Zhabotinsky, A. M. & Epstein, I. R. [1999] "Control of the chlorine dioxide-iodine-malonic acid oscillating reaction by illumination," J. Am. Chem. Soc. 121, 8065-8069.
13. Murray, J. D. [1989] Mathematical Biology (Springer-Verlag, Berlin).
14. Nozakura, T. & Ikeuchi, S. [1984] "Formation of dissipative structures in galaxies," Astrophys. J. 279, 40-52.
15. Ouyang, Q. & Swinney, H. L. [1991] "Transition from a uniform state of hexagonal and strippes Turing pattern," Nature 352, 610-612.
16. Rudovics, B., Barillot, E., Davies, P., Dulos, E., Boissonade, J. & DeKepper, P. [1999] "Experimental studies and quantitative modeling of Turing patterns in the (chlorine dioxide, iodide, malonic-acid) reaction," J. Phys. Chem. A103(12), 1790-1800.
17. Sanz-Anchelergues, A., Zhabotinsky, A. M., Epstein, I. R. & Muñuzuri, A. P. [2001] "Spatially-correlated-noise-induced Turing pattern formation," Phys. Rev. E63, 56124.
18. Turing, A. M. [1952] "The chemical basis of morphogenesis," Philos. Trans. R. Soc. London B327, 37-72.