Abstract
Turing structures and turbulence are analyzed within the framework of a model for the chlorine dioxide—iodine—malonic acid reaction. This reaction has recently provided the first experimental results on the formation of stationary chemical patterns under laboratory conditions. The model is distinguished from previously studied simple reaction-diffusion models by showing a strongly subcritical transition to stripes. This makes it possible for a great variety of localized structures to emerge and be stable. The dynamics of phase singularities and the formation and breakdown of chemical spirals are investigated.
Similar content being viewed by others
References
A. Turing, Phil. Trans. R. Soc. Lond.B327, 37 (1952).
J. D. Murray:Mathematical Biology. Springer-Verlag, Berlin, 1989. For a short review see e.g. J. D. Murray, Bul. Math. Biol.52, 119 (1990).
G. Nicolis and I. Prigogine:Self-Organization in Nonequilibrium Systems, Wiley, New York, 1977.
H. L. Swinney and J. P. Gollub (eds.):Hydrodynamic Instabilities and Transition to Turbulence, Springer, Berlin, Second Edition 1985.
P. Manneville:Dissipative Structures and Weak Turbulence, Academic Press, Boston, 1990.
A. C. Newell and J. V. Moloney:Nonlinear Optics, Addison-Wesley, Redwood City, 1992.
G. M. Edelman:Topobiology. An Introduction to Molecular Biology, Basic Books, New York, 1988.
H. Meinhardt:Models of Biological Pattern Formation, Academic Press, London, 1982.
R. J. Field and M. Burger (eds.):Oscillations and Traveling Waves in Chemical Systems, Wiley and Sons, New York, 1985.
S. C. Müller, Th. Plesser and B. Hess, Science230, 661 (1985).
Z. Noszticzius, W. Horsthemke, W. D. McCormick, H. L. Swinney, and W. Y. Tam, Nature (London)329, 619 (1987).
V. Castets, E. Dulos, J. Boissonade, and P. De Kepper, Phys. Rev. Lett.64, 2953 (1990).
Q. Ouyang and H. L. Swinney, Nature (London)352, 610 (1991).
R. D. Vigil, Q. Ouyang, and H. L. Swinney, Physica A188, 17 (1992).
I. Lengyel, S. Kádár, and I. R. Epstein, Science259, 493 (1993).
O. Jensen, V. O. Pannbacker, G. Dewel, and P. Borckmans, Phys. Lett. A179, 91 (1993).
V. O. Pannbacker, O. Jensen, G. Dewel, P. Borckmans, and E. Mosekilde, in Proc. NATO ARW onSpatio-Temporal Patterns in Nonequilibrium Complex Systems, Santa Fe, New Mexico, April 13–17, 1993
P. Borckmans, G. Dewel, and A. De Wit inSeeds: Genesis of Natural and Artificial Forms, Le Biopole Végétal, Amiens, 1991.
A. De Wit, G. Dewel, P. Borckmans, and D. Walgraef, Physica D61, 289 (1992).
P. Borckmans, A. De Wit, and G. Dewel, Physica A188, 137 (1992).
I. Lengyel, G. Rábai and I. R. Epstein, J. Am. Chem. Soc.112, 4606 (1990).
I. Lengyel, G. Rábai and I. R. Epstein, J. Am. Chem. Soc.112, 9104 (1990).
I. Lengyel and I. R. Epstein, Proc. Natl. Acad. Sci. USA89, 3977 (1992).
A. Hunding and P. G. Sørensen, J. Math. Biol.26, 27 (1988).
F. H. Busse, J. Fluid Mech.30, 625 (1967).
L. M. Pismen, J. Chem. Phys.72, 1900 (1980).
N. I. Meyer and E. Mosekilde, Phys. Lett. A24, 155 (1967).
V. Dufiet and J. Boissonade, Physica A188, 158 (1992).
O. Jensen, V. O. Pannbacker, E. Mosekilde, G. Dewel, and P. Borckmans, Phys. Rev. E50, 736 (1994).
Y. Pomeau, Physica D23, 3 (1986).
O. Thual and S. Fauve, J. Phys. France49, 1829 (1988).
J. J. Perraud, K. Agladze, E. Dulas, and P. De Kepper, Physica A188, 1 (1992).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jensen, O., Pannbacker, V.O., Mosekilde, E. et al. Turing structures and turbulence in a chemical reaction-diffusion system. Open Syst Inf Dyn 3, 215–235 (1995). https://doi.org/10.1007/BF02228817
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02228817