Abstract
A mechanism and a model of a ferroin-catalyzed oscillating chemical system are descrined. This reaction presents an excellent example of a far-from-equilibrium system that forms spatial and temporal dissipative structures. The model shows that while the well-stirred system has a unique and stable stationary state, the same reagent spread in a thin layer may form complex spatiotemporal paterns. Stationary periodic patterns of both small and large amplitude, standing waves, and inhomogeneous chaotic oscillations are found in the model.
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References
I. Prigogine,Introduction to Thermodynamics of Irreversible Process (Thomas, Springfield, Illinois, 1955).
P. Glansdorf and I. Prigogine,Thermodynamic Theory of Structure, Stability and Fluctuations (Wiley-Interscience, 1971).
B. P. Belouson,Zb. Ref. Rad. Med. 1958:145.
A. M. Zhabotinsky,Dokl. Akad. Nauk SSSR 157:392 (1964).
A. N. Zaikin and A. M. Zhabotinsky,Nature 225:535 (1970).
A. M. Zhabotinsky and A. N. Zaikin,Oscillatory Processes in Biological and Chemical Systems (Puschino, 1971), p. 279 (in Russian).
A. T. Winfree,Science 175:634 (1972).
R. J. Field, E. E. Körös, and R. M. Noyes,J. Am. Chem. Soc. 94:8649 (1972).
A. B. Rovinsky and A. M. Zhabotinsky,Teor. Eksp. Khim. 14:182 (1978).
A. B. Rovinsky and A. M. Zhabotinsky,Teor. Eksp. Khim. 15:25 (1979).
Z. Noszticius, H. Farkas, and Z. Shelly,J. Chem. Phys. 80:6062 (1984).
L. Kuhnert, H.-J. Krug, and L. Pohlmann,J. Phys. Chem. 89:2022 (1985).
A. B. Rovinsky and A. M. Zhabotinsky,J. Phys. Chem. 88:6081 (1984).
A. B. Rovinsky,J. Phys. Chem. 90:217 (1986).
A. Turing,Phil. Trans. R. Soc. 237B:37 (1952).
A. B. Rovinsky and A. M. Zhabotinsky, inFundamental Research in Chemical Kinetics, A. E. Shilov, ed. (Gordon and Breach, 1986).
A. B. Rovinsky,J. Phys. Chem. 88:4 (1984).
F. Ariese and Z. Nagi-Ungvarai,J. Phys. Chem. 90:1 (1986).
F. Ariese and Z. Nagi-Ungvarai,J. Phys. Chem. 90:1496 (1986).
R. J. Field and H.-D. Försterling,J. Phys. Chem. 90:5400 (1986).
G. Ioss and D. Joseph,Elementary Stability and Bifurcation Theory (Springer-Verlag, 1980).
B. D. Hassard, P. D. Kazarinoff, and J.-H. Wan,Theory and Application of Hopf Bifurcation (Cambridge University Press, 1981).
L. P. Shilnikov,Matem. Zb. 61:104, 433 (1963).
L. P. Shilnikov,Dokl. Akad. Nauk USSR 170:49 (196).
L. P. Shilnikov,Matem. Zb. 77:461 (1968).
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Zhabotinsky, A.M., Rovinsky, A.B. Mechanism and nonlinear dynamics of an oscillating chemical reaction. J Stat Phys 48, 959–975 (1987). https://doi.org/10.1007/BF01009526
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DOI: https://doi.org/10.1007/BF01009526