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Temporal oscillations in a kinetic model of the Belousov-Zhabotinskii reaction

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References

  • [1955] L. Flatto & N. Levinson, Periodic Solutions of Singularly Perturbed Systems. J. Rational Mach. Anal., 4, 943–950.

    Google Scholar 

  • [1959] B. P. Belousov, Sb. Ref. Rediat. Med. Medgiz. Moscow, 145.

  • [1960] F.R. Gantmacher, The Theory of Matrices, Vol. II. New York: Chelsea.

    Google Scholar 

  • [1960] V. Nemytskii & V. Stepanov, Qualitative Theory of Ordinary Differential Equations. Princeton: University Press.

    Google Scholar 

  • [1964] A. Zhabotinskii, Periodic Oxidation Reactions in Liquid Phase, Dokl. Akad. Nauk. SSSR 157, 342.

    Google Scholar 

  • [1967] R. Abraham & J. Robbin, Transversal Mappings and Flows. New York: W.A. Benjamin.

    Google Scholar 

  • [1967] R. Abraham & J. Marsden, Foundation of Mechanics. New York: W.A. Benjamin.

    Google Scholar 

  • [1967] F. Heineken, H. Tsuchiya & R. Aris, On the Mathematical Status of the Pseudo Steady State Hypothesis of Biochemical Kinetics. Math. Biosciences 1, 95–113.

    Google Scholar 

  • [1969] H.G. Busse, A Spatial Homogeneous Chemical Reaction. J. Phys. Chem. 73, 750.

    Google Scholar 

  • [1970] A. Zaiken & A. Zhabotinskii, Concentration Wave Propogation in Two Dimensional Liquid Phase Self-Oscillatory Systems. Nature 225, 535–537.

    Google Scholar 

  • [1972] R. Field, E. Körös & R. Noyes, Oscillations in Chemical Systems II, Thorough Analysis of Temporal Oscillation in the Bromate-Cerium-Malonic Acid System. J. Amer. Chem. Soc. 99, 8649–8664.

    Google Scholar 

  • [1972] A.T. Winfree, Spiral Waves of Chemical Activity. Science 175, 634–636.

    Google Scholar 

  • [1973] N. Kuiper & J. Robbin, Topological Classification of Linear Endomorphisms. Inventiones Math. 19, 83–106.

    Google Scholar 

  • [1974] R. Field & R. Noyes, Oscillations in Chemical Systems IV. Limit Cycle Behavior in a Model of a Real Chemicl Reaction. J. Chem. Phys. 60, 1877–1884.

    Google Scholar 

  • [1974] H. Hahn, Geometrical Aspects of the Pseudo Steady State Hypothesis in Enzyme Reactions. Lecture Notes in Biomath. 4, 328–345.

    Google Scholar 

  • [1975] R. Field, R. Noyes & D. Edelson, Mechanistic Details of the Belousov-Zhabotinskii Oscillations. Int. J. of Chem. Kinetics, Vol. VII, 417–432.

    Google Scholar 

  • [1975] S.P. Hastings & J.D. Murray, The Existence of Oscillatory Solutions in the Field-Noyes Model for the Belousov-Zhabotinskii Reaction. SIAM J. Appl. Math. 28, 678–688.

    Google Scholar 

  • [1976] S.P. Hastings, Periodic Plane Waves for the Oregonator. Studies in App. Math. 55, 293–299.

    Google Scholar 

  • [1976] M. Hirsch, Differential Topology. New York: Springer-Verlag.

    Google Scholar 

  • [1976] I. Hsü & N. Kazarinoff, An Applicable Hopf Bifurcation Formula and Instability of Small Periodic Solutions of the Field-Noyes Model. J. Math. Anal. Appl. 55, 61–89.

    Google Scholar 

  • [1976] W. Troy, Threshold Phenomena in the Field-Noyes Model of the Belousov Zhabotinskii Reaction. To appear.

  • [1976] J. Tyson, The Belousov-Zhabotinskii Reaction. Lecture Notes in Biomath. To appear.

  • [1976] R.J. Wolfe, Oscillations in a Detailed Kinetic Model of the Belousov Zhabotinskii Reaction. Ph.D. Thesis, SUNY at Buffalo.

  • [1977] W. Troy & R. Field, The Amplification Before Decay of Perturbations Around Stable States in a Model of the Zhabotinskii Reaction. SIAM J. Appl. Math. 32, 306–322.

    Google Scholar 

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Communicated by B.D. Coleman

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Wolfe, R.J. Temporal oscillations in a kinetic model of the Belousov-Zhabotinskii reaction. Arch. Rational Mech. Anal. 67, 225–250 (1978). https://doi.org/10.1007/BF00253149

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